The league, meeting in Cairo, also called on Syria to form a national unity government with the opposition within two months.
A government official called the plan “flagrant interference” in Syria’s internal affairs, state TV said.
The UN says more than 5,000 people have died as a result of the crackdown on protests since they began last March.
The league called on both sides to end the bloodshed.
The government in Damascus says it is fighting “terrorists and armed gangs” and claims that some 2,000 members of the security forces have been killed.
Arab League split
“Syria rejects the decisions taken which are outside an Arab working plan, and considers them an attack on its national sovereignty and a flagrant interference in internal affairs,” the unnamed Syrian official said.
The official said the Arab League proposals were not in the interests of the Syrian people and would not prevent the country from “advancing its political reforms and bringing security and stability to its people who have shown, during this crisis, their support for national unity as they have rallied around President Assad”.
Saudi Arabia said it was pulling out of the league’s 165-strong monitoring mission in Syria because Damascus had broken promises on peace initiatives.
While the Arab League ministers said they were extending the controversial mission for another month, analysts say the Saudi decision has thrown its longer-term future into serious doubt.
Saudi Arabia is one of the key founders of the league’s projects, but the monitors have been criticised for failing to stop the violence.
The Arab League is now increasingly split about what could be done to resolve the Syrian crisis, the BBC Middle East editor Jeremy Bowen in Damascus reports.
With the Syrians rejecting the conditions of the initiative, the Arab League’s roadmap is effectively in tatters, our correspondent says.
Meanwhile, violence has continued in Syria, with activists reporting battles between government troops and army defectors in Damascus’ suburb of Douma on Sunday.
At least five people were killed, according to Syria’s Local Coordination Committees.
Activists say almost 1,000 people have been killed since the monitoring mission began in December.
‘No military intervention’
At the Arab League meeting, Saudi Foreign Minister Prince Saud al-Faisal urged the international community to step in and put pressure on Damascus.
Qatari ruler Sheikh Hamad bin Jassim al-Thani read out a statement agreed by the ministers laying out an ambitious plan of political reform.
It called on President Assad to delegate power to his vice-president to engage in proper dialogue with the opposition within two weeks, and form a government of national unity in two months.
The league said this should eventually lead to multi-party elections overseen by international observers.
“The new Arab initiative adopted by the foreign ministers envisages the peaceful departure of the Syrian regime,” Sheikh Hamad said, in a quote translated by the AFP news agency.
He said the league would seek the support of the UN Security Council for the changes.
But he added: “We’re not talking about military intervention.”