Mayor Marion Barry and City Council Chairman David A. Clarke, grappling with the city's mounting financial difficulties, yesterday discussed ways to persuade the city's 30,000 unionized employes to forgo part of a pay increase of 6 to 9 percent scheduled to take effect in October.

Clarke raised the subject of reopening contract negotiations with city employes during a private meeting between Barry and City Council members to review Barry's proposed budget for fiscal 1984, according to participants in the meeting.

Barry indicated he would favor such a move, but said he wanted to hold off until after the council had approved his new budget, participants in the meeting said. The council has 50 days to approve the budget.

Clarke and several other council members said they favor trying to reopen contract negotiations now, in hopes of reducing the city's personnel costs and using that money for social service programs that Barry wants to cut.

"The council is going to have to start looking at working with the mayor to renegotiate contracts at a lower-than-expected pay raise," said one council member who attended the afternoon session in the mayor's office and asked not to be named.

According to a high-ranking D.C. government source, Barry privately indicated recently that he was interested in finding a way to reopen contract negotiations to cut back the scheduled raises--possibly in return for a promise not to reduce services for the poor or to substantially raise taxes.

Barry's proposed budget contains service cuts, and he indicated this week that contrary to earlier promises, he may consider asking the council to increase property taxes.

Barry declined yesterday to comment on his plans. However, prior to the session in the mayor's office, Clarke said he would favor returning to the bargaining table with city employes if it were done before the council acts on the mayor's budget.

"I'm in favor of sitting down with labor representatives and seeing whether an accommodation can occur, but it should be done before" the new budget is approved, Clarke said. "Unions all across the country are having to look at the possibility of RIFs and reconsider the benefits of pay increases."

Barry's $1.99 billion budget proposal includes a 7 percent pay increase for all city workers, at a total cost of about $65 million, but does not earmark sufficient revenues to cover the increase in most agencies.

Earlier yesterday, at a meeting with 200 representatives of unionized employes, Barry stuck to his campaign pledge to grant workers a pay increase next year and not to lay off any full-time city employes.

Top officials of the public employe and teachers unions that represent most city workers said yesterday they knew nothing about plans to reopen contract talks.

"I would be dumbstruck if he Barry tried to reopen talks," said Bernard Demczuk, legislative representative for the American Federation of Government Employees and a staunch Barry ally. He said that while members might be willing to discuss productivity or a tax increase, "We will not accept anything less than 7 percent pay raises and no layoffs."