Sheik Ahmad Moaz al-Khatib said his offer was conditioned on the government meeting two demands: the release of 160,000 prisoners held by the government and the renewal of all expired passports held by Syrians abroad, The New York Times reported.
The newspaper said the passport demand apparently was to help expatriates and exiled opposition leaders who could not travel to Syria even if they wanted.
The offer was posted on Khatib's Facebook page.
The Times said it quickly drew criticism from others in the Syrian opposition coalition, saying Khatib had not consulted with them in advance. In the face of the criticism, the sheik said he was only expressing a personal opinion.
There was no was no immediate comment from the Syrian government. The Times said Khatib is a respected Sunni cleric, once the imam of the historic Umayyad mosque in Damascus. His coalition, has been formally recognized by the Arab League, the European Union and the United States.
Also Wednesday, world leaders met in Kuwait to try to raise $1.5 billion in humanitarian aid for Syria as activists reported Syrian planes bombed several cities.
The opposition Local Coordination Committees of Syria said government warplanes attacked cities across Syria, including Idlib, where cluster bombs reportedly were used, CNN reported.
Cluster bombs explode in the air and rain dozens, or possibly hundreds, of smaller bombs over an area the size of a football field. Syria has denied using cluster bombs in the conflict.
Syria's state-run media reported government forces killed dozens of terrorists -- the government's term for anti-government forces -- outside Damascus.
The United Nations and world leaders meeting in Kuwait discussed shortfalls in aid for refugees, CNN reported.
Kuwaiti Emir Sheik Sabah al-Ahmed al-Sabah started the conference by announcing a $300 million donation. Other pledges followed, including Germany with $10 million, the United Arab Emirates with $300 million and Bahrain with $20 million.
President Barack Obama announced Tuesday the United States would kick in an additional $155 million in aid for Syrians inside the country and the more than 500,000 refugees who have fled the nearly two years of violence. The new funding brings the total U.S. pledge to $365 million.
So far, only a fraction of the funding for 2013 has been received, U.N. officials said, limiting the ability of U.N. agencies and their partners to reach people "who desperately need help."
Other groups said getting the money is only part of the problem, CNN said.
Doctors Without Borders said in a statement Tuesday international aid "is not being distributed equitably between government- and opposition-controlled areas. Areas under government control receive nearly all international aid, while opposition-held zones receive only a tiny share."
The International Committee of the Red Cross said it's doing the best it can to ensure aid is delivered fairly, CNN reported.
"Usually when we do the distribution, we try to be present, or if we can't because of the security measures, we monitor the distribution very closely," spokeswoman Dibeh Fakhr said Wednesday. "The security is deteriorating very rapidly, and this is why we are not present everywhere in the country. But we are doing our best."