Finance ministers from the Arab League are meeting in Egypt to discuss possible sanctions against Syria.
The organisation had set a Friday deadline for Damascus to allow rights monitors into the country, but the deadline passed with no firm commitment from Syrian officials.
Sanctions could include halting flights and imposing a freeze on financial dealings and assets.
Commenting on the threat of sanctions, Syrian Economy Minister Mohammed Nidal al-Shaar said: "If that is to happen, it will be very unfortunate because the damage will be to all sides".
But "we don't expect all Arab countries to yield or participate in sanctions," he told the AFP news agency. "In fact, we are almost certain that some Arab countries will not participate."
Lebanon has already made clear that it will not enforce any economic sanctions against its neighbour, and Iraqi Foreign Minister Hoshyar Zebari said on Saturday that it was "not possible" to impose economic sanctions on Syria due to its commercial ties with Iraq and the large number of Iraqi refugees there.
"We announce our reservation on this issue," he told reporters, although it was not immediately clear if he meant that Iraq would refuse to enforce a proposed package of Arab sanctions, which was to be discussed by finance ministers on Saturday and foreign ministers on Sunday.
As the deadline expired on Friday, fresh anti-government protests were reported in various towns across Syria and activists said up to 26 people had been killed, most of them in the central province of Homs.
The province also saw an ambush which led to the killing of 10 security personnel, including six elite military pilots, according to the Syrian armed forces quoted by the state-run SANA news agency.
Al Jazeera's Hashem Ahelbarra reports from
a refugee camp on the Turkish border with Syria
The military blamed "terrorists" for the attack, and threatened to "cut every evil hand" that targets the country's security.
"The armed forces will continue to carry out its mission ... and will cut every evil hand that targets Syrian blood." it said in a statement.
The Syrian leadership blames the unrest in the country on a foreign plot, saying "armed terrorists" are driving the uprising.
The Associated Press news agency reported that rather than signing the Arab League agreement, Syria had sent a letter to the office of Nabil el-Araby, the bloc's secretary-general, seeking more details about the proposed observer mission and its legal status.
The US and the European Union have already imposed major sanctions, including an oil embargo, on the Syrian leadership.
Al Jazeera's Zeina Khodr, reporting from the Lebanese capital, Beirut, said punitive measures by the Arab League would likely hurt the Syrian government, especially since the economy is already under strain.
"Major sources of revenue from the oil and tourism sectors have already been affected," she said.
"But a Western diplomat said that the real aim for these sanctions is trying to convince the business community, the middle class in Syria which has so far been supporting the Syrian president, to switch sides.
"Their support may not stem from the fact that they believe in a one-party rule but simply because they fear the alternative, especially since the opposition has become an armed movement and there are fears that the country could slide towards a civil war."
SANA dismissed the ultimatum, saying that the Arab League had become a "tool for foreign interference."
The news agency also said thousands of people were demonstrating in support of the government in cities across the country.
'No more tolerance'
Turkey's foreign minister hinted on Friday that he could attend a meeting of Arab League foreign ministers at which possible sanctions could be discussed, and said Ankara was considering taking further steps against Syria in conjunction with the bloc.
"We have a road map that we have agreed on with the Arab League," Ahmet Davutoglu said. "I want to say clearly we have no more tolerance for the bloodshed in Syria."
Al Jazeera’s Hashem Ahelbarra, reporting from the Turkish province of Hatay on the border with Syria, said he was in a refugee camp when news broke that Assad refused to sign the deal.
"People there were saying that this should provide the international community a sense of clarity, [that it has] to move forward and impose sanctions coupled with a military intervention.
"Refugees have been there for five months. They do not want to stay there forever. They know that for Assad’s regime to collapse, there need to be international intervention coupled with support to army defectors."
The United Nations says more than 3,500 people have been killed since the start of the uprising in March.
Most foreign media has been barred from entering Syria, making it difficult to independently verify reports.