Tripoli, Libya (CNN) -- Curt Weldon, the former U.S. congressman who intends to meet with Moammar Gadhafi and persuade him to step aside, told CNN on Thursday he hasn't yet but still hopes to sit down with Libya's defiant strongman.
If and when he does have the sit-down, Weldon said he plans "to reinforce the message of the Obama administration."
Later Thursday, Weldon told "The Situation Room" he will give the Libyan government until Friday to set up the meeting.
"It is time for us to resolve this conflict," said Weldon, a Republican who once represented a House district outside Philadelphia. Libya remains in a deadly stalemate as pro-Gadhafi forces battle rebel fighters demanding an end to Gadhafi's nearly 42-year-rule.
Weldon said he was underscoring the importance of an immediate cease-fire monitored by the United Nations on both sides, with the Libyan army pulling back in all the cities in distress and rebel forces stopping their forward movement to protect the people.
"I'm here only because I want to avoid war," Weldon told CNN's Wolf Blitzer. "I don't want to see American soldiers killed, and I don't want to see more innocent Libyans killed."
Weldon said he and his small entourage have met with aides and other officials of the embattled regime this week, including the prime minister, chief of staff and one of Gadhafi's sons, Saadi.
"We are here on a private delegation only because I have met with Gadhafi more than any other American on three official congressional visits. I know the man and I wanted to basically have the chance to confront directly the issues that are important," he said.
Gadhafi sent a letter to President Barack Obama on Wednesday urging him to stop NATO's bombing in Libya. Weldon, who appeared Thursday on CNN's "American Morning," was asked whether Libyan officials are hearing his message.
"Well, they have no choice but to hear me," he said. He said he wanted to have a face-to-face meeting with Gadhafi because it would convey the "gravity of the situation."
"Time is running out. The world is very concerned about what's happening in Misrata. I have been to Misrata. The world is very concerned about what's happening in Benghazi and all of the communities. We don't want more Libyan people to die," Weldon said. Misrata has been wracked by warfare, and Benghazi is the center of the opposition movement.
Weldon, who wrote an op-ed piece in The New York Times on Wednesday detailing his stance on the conflict, said now is the time to pursue a meeting, but he realizes there is uncertainty and security concerns may determine whether a sit-down will occur.
"In my previous meetings with Gadhafi, you never know until the last moment that you are going to have the meeting. We are here, and we are available for the rest of tonight and into tomorrow. So there is no other excuse now. We are here to give a message," Weldon said.
Weldon said that in addition to Gadhafi's resignation, a cease-fire on both sides, a withdrawal of government forces from key cities and no further advances by rebel forces, he has voiced other proposals.
They include a joint interim government run by Libya's current prime minister and the opposition leader; unfettered humanitarian access; and the establishment of a parliamentary commission that would include American, Mideast, European and African politicians helping to establish a new parliament in Libya.
As far as the Gadhafi family, Weldon's proposals also suggest a possible title for Gadhafi as honorary chairman of the African Union and allowing his second-oldest son, Saif, to stand in elections.
Saif al-Islam Gadhafi was once thought of as a leading reformer in the Libyan government, but the 38-year-old has become one of his father's most outspoken defenders since the start of the unrest. Weldon said he favors an international tribunal to look at any possible human rights violations by key leaders, including Saif.
"In a fair election, up until now, he (Saif) should be given the opportunity to seek office where he can run against other candidates, perhaps for the presidency," Weldon told CNN.
Weldon told Blitzer U.S. individuals paid for his airfare, and he has received no money from the Gadhafi family.
In 2004, Weldon led a congressional delegation to Tripoli and met privately with Gadhafi after the Libyan leader renounced terrorism in an effort to establish warmer ties with the West. Weldon said in his Times opinion piece Wednesday that he traveled in 2004 to support Gadhafi's decision to give up Libya's nuclear weapons program, though neither he nor the White House wanted to support Gadhafi himself.