Prime Minister Saad al-Hariri warned in a statement earlier of "legal consequences" for strikers who jeopardised work at state institutions.
A decision on the central bank workers' next step would be taken at their general assembly meeting on Tuesday, Abbas Awada, head of their syndicate, said in an interview with the broadcaster al-Jadeed.
He said there had been negative effects from the move and pressure "on the market, on the governor of the central bank, and on all Lebanese".
"A positive decision" may be taken to "facilitate matters", he said, but added that if the government approved the budget without addressing their concerns "we will proceed in an open strike".
Central bank governor Riad Salameh convened a meeting with central bank employees where it was agreed to open Lebanese pound pricing operations against foreign currencies and to reopen financial transfers, the state-run National News Agency reported. The pound is pegged against the U.S. dollar.
Salameh opposed the strike action and had asked for it to be lifted, Awada said.
Marwan Mikhael, chief economist of Lebanese investment bank Blominvest, said banks retain access to liquidity through the interbank market, but cheque clearing operations had stopped.
"It will have an impact eventually, but I think for the short term it will be fine," he said.
Finance Minister Ali Hassan Khalil has said the draft budget involves "wide reductions" in spending based on the need for "exceptional austerity measures".
The draft budget proposals include annulling performance-linked bonuses paid in some state-run institutions, including the Central Bank. In some cases, these have amounted to several months extra salary a year.
Government officials from Lebanon's rival political parties have all stressed the need to enact immediate reforms to prevent an economic crisis. Lebanon's public debt burden is one of the highest in the world, equivalent to about 150 percent of gross domestic product.
(Reporting by Tom Perry, Laila Bassam and Angus McDowall; Editing by Toby Chopra, Hugh Lawson, William Maclean) ((mailto:firstname.lastname@example.org; Reuters Messaging: rm://email@example.com))