A U.S. lawmaker introduced legislation Wednesday to strip former President Jimmy Carter's Georgia-based scholarly institution of taxpayer support because of Carter's plans to meet with the top leaders of the Palestinian terror group Hamas.

And a second lawmaker presented a non-binding resolution that would urge former presidents from "freelance diplomacy" in direct response to Carter's visit.

Carter is set to set to meet Thursday with Mahmoud Zahar, a top Hamas leader with control over militants in the Gaza Strip, and he met Tuesday with a high-ranked Hamas politician.

But the heaviest criticism for Carter is coming over a planned meeting on Friday with Hamas' exiled leader Khaled Meshal.

"America must speak with one voice against our terrorist enemies," Rep. Joe Knollenberg, R-Mich., said in a statement from his office. "It sends a fundamentally troubling message when an American dignitary is engaged in dialogue with terrorists. My legislation will make sure that taxpayer dollars are not being used to support discussions or negotiations with terrorist groups."

Knollenberg said the Carter Center has received about $19 million in taxpayer funds since 2001. He named his bill the Coordinated American Response to Extreme Radicals Act — or CARTER Act, for short. The Carter Center is housed at Emory University in Atlanta.

The non-binding legislation was forwarded by Rep. Bill Shuster, R-Pa. If adopted, the bill would express the "sense of Congress" that it "disapproves of former President Jimmy Carter's freelance diplomatic efforts in the Middle East, which contradict the stated foreign policy position of the current Administration."

The new legislation is the latest embodiment of scorn directed at Carter over meetings he plans this week with leaders of Hamas, which both the United States and Israel recognize as a terror organization and with which they refuse to negotiate.

Also Wednesday, Reps. Howard Berman, D-Calif., who is chairman of the House Foreign Affairs Committee, and Gary Ackerman, D-N.Y., chairman of the Foreign Affairs Mideast subcommittee, wrote Carter imploring him not to meet with any more Hamas officials.

"[T]his visit will undermine the Middle East peace process and damage the credibility of Palestinian moderates," they wrote, adding that the "legitimacy and prestige that Hamas will derive from your visit will be seen in the region as a clear demonstration that violence pays."

Rep. Artur Davis, D-Ala., told FOX News, "I don't think Israel should try to negotiate with Hamas because Hamas does not recognize Israel's right to exist." Davis added that Carter's overtures stood athwart a tradition of support for Israel in America.

On Tuesday, more than 50 House members wrote Carter urging him to not meet with Meshal, calling him the man behind the deaths of 26 Americans.

Sen. Barack Obama, who has stated his disagreement with Carter on the Hamas visit but supports an open dialogue with Iran, was pressed Wednesday on the difference between the two.

"[T]here is a distinction in terms of their status within the international community," he told a group of Jewish community leaders in Philadelphia. "Hamas is not a state. Hamas is a terrorist organization. They obviously have developed great influence within the Palestinian territories, but they do not control the apparatus of power," he said.

A Hamas spokesman, Ismail Radhwan, said in an interview that Carter's visit "reflects the recognition that the Hamas movement cannot be ignored," according to a transcript from MEMRI TV. "We will benefit from this meeting by explaining our cause, our positions, and our principles and by presenting our just cause," the spokesman said.

Carter, speaking briefly with FOX News on Wednesday, said the search for Mideast peace should include reaching out to groups such as Hamas. The former president was the broker of Israel's peace treaty with Egypt three decades ago.

"I'm going to try to get Syria to be constructive in the entire peace process, that would include Iraq and Lebanon, as well," he said.

The Islamic militant group will meet with Carter in Cairo about their demand that Israel open Gaza's crossings and stop military raids in the territory, a Hamas official told FOX News.

The meeting is expected to include Zahar, which would be significant because he controls militants in Gaza and is crucial to cease-fire negotiations with Israel. Egypt is trying to broker those talks.

Zahar is also instrumental to talks on the release of the captured Israeli soldier Cpl. Gilad Shalit, whose 2006 capture by Hamas was a catalyst to the monthlong fighting between Israel and the Iran-backed terror group Hezbollah, which also captured Israeli soldiers. Hamas wants some 450 Israeli-held Palestinian prisoners in exchange for Shalit's release.

When speaking with FOX earlier Wednesday, Carter sidestepped a question about about how his talks are shaping up Friday with Meshal.

"I'd rather not tell FOX News what I want to talk to," Carter said. "I don't know yet. We haven't firmed up anything. So it's premature to talk about that yet."

Carter reportedly hugged and kissed another Hamas leader Tuesday in the West Bank town of Ramallah. Carter's embrace of Nasser Shaer, a senior Hamas politician, at a closed-door reception organized by Carter's office was reported by several news outlets.

"He gave me a hug. We hugged each other, and it was a warm reception," Shaer told The Associated Press. "Carter asked what he can do to achieve peace between the Palestinians and Israel ... and I told him the possibility for peace is high."

Shaer, who served as deputy prime minister and education minister in the Hamas-led Palestinian government that unraveled last year, is considered a leading member of the Islamic militant group's pragmatic wing. After a stint in an Israeli prison last year, he is now a professor at a West Bank university, teaching comparative religion.

Carter also laid a wreath at the grave of Yasser Arafat, whom he praised as a man who fought for "just causes" in the world. The Bush administration and many Israelis blame Arafat for the breakdown of peace talks seven years ago and the violence that followed.

President Bush did not visit Arafat's mausoleum in Ramallah when he visited earlier this year.

Israel and the West Bank were the first stops on a visit that also is to include Saudi Arabia, Egypt, Jordan and Syria — where the virulently anti-Israel Hamas movement is headquartered.

FOX News' Reena Ninan and The Associated Press contributed to this report.