Former House Speaker Newt Gingrich said he hopes to jump into the race for president "within a month," noting that he's already made visits to key states like Iowa and New Hampshire and has beefed up his political staff.

"I think within a month, we will have that taken care of and we'll be running," Gingrich said.

In some of his strongest statements to date about his political intentions, Gingrich talked on "Fox News Sunday" about laying the groundwork for a 2012 presidential campaign. Gingrich is one of several Republican heavyweights expected to end the water-testing phase in the next few months and make clear whether they're running.

"The water's pretty warm," Gingrich said Sunday." "My hope is that within a month that we'll be in swimming very rapidly."

Fox News has learned that Gingrich may bypass the exploratory committee phase of a presidential campaign and go straight to announcing his candidacy.

In the interview Sunday, Gingrich tried to reconcile seemingly conflicting statements he's given about U.S. military involvement in Libya. Gingrich earlier said the United States should back a no-fly zone. After President Obama sent in the U.S. military to help establish one, Gingrich said he would not have supported intervention.

Asked to clarify, Gingrich said Sunday that the United States should have been for replacing Libyan leader Muammar al-Qaddafi without using the military. But he said now that the United States is involved militarily, the goal should be to replace Qaddafi.

"If you're not in the lake, don't jump in. Once you're in the lake, swim like crazy," he said.

Gingrich also acknowledged voters may have concerns about his past, including his marital infidelity. He repeated that he has sought "God's forgiveness." But he also defended his role leading the charge against former President Bill Clinton over his affair, saying he didn't believe that role was hypocritical since the Clinton impeachment centered around the issue of perjury.

"The question I raised was very simple -- should a president of the United States be above the law?" he said. "I don't think a president of the United States can be above the law."