Portugal's PM has presented the president with what he calls an agreed "deal" to keep his coalition intact.
PM Pedro Passos Coelho says his centre-right governing partner pledged to keep supporting his government after two resignations plunged it into crisis.
The uncertainty had sent the interest rate on Portuguese 10-year bonds above 8%, before falling back to 6.8%.
Any deal would have to be approved by President Anibal Cavaco Silva, who is due to meet the parties on Monday.
The government is struggling to fulfil tough bailout conditions.
Portugal received a bailout worth more than 78bn euros ($102bn; £67bn) in May 2011, on the condition it implemented austerity measures.
"The prime minister presented to Cavaco Silva a political deal reached with the leader of [the ruling coalition's junior partner, the centre-right Popular Party] CDS-PP," said a government spokesman.
He provided no details on the agreement, but said a statement would be released after the two parties held talks on Saturday.
Portugal's latest uncertainty had rekindled market anxiety that the country might need further international assistance, putting new pressure on the eurozone.
Later on Friday the credit rating agency, Standard and Poor's, said it could lower its credit rating on Portugal "if growing political uncertainty slows its structural fiscal adjustment process and undermines support from official lenders, including the European Union and International Monetary Fund".
A credit rating is a judgment on a borrower's ability to repay its debts.
On Thursday night Mr Passos Coelho, leader of the Social Democratic Party, said a "formula [had] been found to maintain the government's stability". He was speaking after crisis talks with President Anibal Cavaco Silva. He did not explain what that formula meant.
Earlier he held a series of meetings with Paulo Portas of the CDS-PP, who resigned as foreign minister on Tuesday.
Mr Passos Coelho, who refused to accept Mr Portas's resignation, said the latter had told him "it was a personal decision and does not involve the support of the CDS-PP for the government".
President Cavaco Silva is due to begin talks with the parties on Monday.
Germany's Finance Minister, Wolfgang Schaeuble, said he did not expect contagion to spread from Portugal to other eurozone countries.
"I think the euro is now viewed on the world's financial markets as so stable that domestic political situations in individual countries... don't mean a crisis for the stability of the euro as a whole,'' he said in Berlin.
European Central Bank President Mario Draghi praised the Portuguese government's efforts in the debt crisis.
"Certainly, it's been a painful route - and the results that have been achieved have been quite significant, remarkable, if not outstanding," he said.
The crisis began on Monday with the resignation of Finance Minister Vitor Gaspar, who for two years had overseen the unpopular austerity policies.
Portugal has been in recession for two years and the economy is expected to contract by 2.3% this year.