"Normal relations" remain out of reach for the Council on American-Islamic Relations and the FBI, officials on both sides say, despite early optimism by the nation's largest Islamic advocacy group that a new administration in the White House would change their strained relationship.

"It has not changed," an FBI official said of his agency's relationship with CAIR. "We're still not maintaining formal liaison relationships with them."

The federal official said a "normal" relationship "could be re-established, but has not yet."

"They've been kind of in stasis, to use a sci-fi term," Ibrahim Hooper, CAIR's national communications director, said of the FBI. "(Relations) haven't gotten worse, haven't gotten better."

Late last year several FBI field offices across the country notified local CAIR chapters that the FBI would be limiting "formal contact" with them because "certain issues must be addressed," as an October 2008 letter to a CAIR office in Oklahoma City stated.

Among the issues, FBI officials were concerned about CAIR's possible ties to Hamas, the militant Palestinian group. According to court documents, at least one current CAIR official attended a Philadelphia meeting of Hamas supporters in 1993, a year before CAIR was founded.

In 2007, CAIR was named an "unindicted co-conspirator" in a terrorism case in which leaders of the Texas-based Holy Land Foundation were later convicted of funneling money to Hamas. 

"(Law enforcement officials) have a duty to be judicious in our activities as representatives of the federal government," reads the letter to CAIR's office in Oklahoma City. "As a result, if CAIR wishes to pursue an outreach relationship with the FBI, certain issues must be addressed to the satisfaction of the FBI."

"We wanted them to basically sit down and say that they didn't support (Hamas) and they intended to refrain from future support," the FBI official said. "That's really nothing fancy, other than an ideological rejection of Hamas. They don't want to (do) that."

The FBI official characterized CAIR's role as an "indirect link to Hamas." 

CAIR officials deny any wrongdoing and blame the Bush administration for giving the group a bad rap. 

"What we're looking at is some Bush administration individuals who wanted to make sure that the relationship between CAIR and law enforcement authorities was going to be harmed (and) put some things in place before they left office," Hooper said. "We're seeing the fallout from that now."

Asked about the assertion that CAIR is unwilling to condemn Hamas, Hooper pointed to a CAIR statement issued in March, on the fifth anniversary of the Madrid, Spain, train bombings that killed nearly 200 people.

"We unequivocally condemn all acts of terrorism, whether carried out by Al Qaeda ... (or) Hamas ... or any other group designated by the U.S. Department of State as a 'foreign terrorist organization,'" the March statement said.

Despite that statement as well as one welcoming improved ties -- posted on CAIR's Web site after Obama's inauguration -- CAIR's relationship with the FBI has been "curtailed in one area, which is the outreach area," Hooper said.

"We used to do town hall meetings, we used to do diversity training or other things with the FBI, and those outreach efforts have been curtailed," he said, adding that those outreach efforts helped the FBI understand the Muslim community and vice versa.

But the strained relationship doesn't rule out contact or cooperation between the agency and the advocacy group.

The limited relationship with CAIR "doesn't mean we won't talk to them," the FBI official said.

"It doesn't mean they can't come to us with a civil rights complaint," the official said. "(And) if they have a problem or identify somebody that has a problem or a complaint, they would come to us, and we would listen to them and take their complaint. We wouldn't shut the door in their face and say we can't talk to you."

Hooper said CAIR remains in "regular contact with FBI personnel around the country on issues related to civil rights," an aspect of the FBI-CAIR relationship the bureau has always said would continue despite limits on outreach efforts.

Lines of communication are also still open with the FBI "if we get an e-mail that seems suspicious," he said.

"If we get something that seems to indicate that somebody might be advocating violence or something of that nature, that goes beyond just free-speech issues, we'll turn it over to the FBI," Hooper said. "We'll turn it over to them, as needed and as required by law and ethics of an organization that wants to promote the safety and security of our nation."

In fact, the FBI recently has been "talking with" CAIR about a civil rights issue Hooper is particularly invested in: an alleged death threat made against him.

After the book "Muslim Mafia: Inside the Secret Underworld That's Conspiring to Islamize America" was released last month, Hooper received a fax saying, "Muslim Neanderthal Dougie Hooper (AKA Ibrahim Hooper) will be soon hanged for treason against the United States." 

The fax included a "picture of a hangman's noose," Hooper said.

"We're in touch with (the FBI) on a regular basis" about that, and they are "looking into it," Hooper said.

On Monday, a federal judge ordered self-described anti-terrorism investigator and "Muslim Mafia" author Paul David Gaubatz to remove from his Web site thousands of documents that his son allegedly stole from CAIR. CAIR is currently suing Gaubatz.

Gaubatz was ordered to "promptly return to counsel for CAIR any copies of CAIR's donor and employee lists that were obtained or by Defendant Chris Gaubatz from CAIR's offices or facilities," say court documents obtained by FoxNews.com.

As another example of FBI-CAIR cooperation, Hooper said CAIR's Michigan office "was in touch with (the FBI) to try and cool down the situation" after an FBI raid in Detroit last month turned into a shootout, killing a radical Muslim leader.

Asked for details of CAIR's efforts in the case, Hooper referred questions to his organization's Michigan chapter, which did not return a call from Fox News.