State-chartered savings and loan associations began quietly reopening today after a six-day "bank holiday" -- some with long lines of customers, but with no renewed runs on deposits.

Only one institution, Century Savings Bank, which has four branch offices in the state, reopened for full service under a new Ohio law. There were no signs of panic as a slow but steady stream of customers arrived at deposit windows. Officials said more people made deposits than withdrawals.

Among early customers at a Cincinnati branch was Mayor Charles Luken, who stopped by to make a deposit.

Brian Usher, press secretary to Gov. Richard F. Celeste, said "a handful" of additional S&Ls would be allowed to reopen Friday or Monday and "most, if not all" state-chartered savings associations would open for limited withdrawals Friday.

In his televised press conference last night, President Reagan referred to the forced closing of 70 Ohio savings banks as a local problem that is "limited to Ohio" and does not pose a threat to the U.S. banking system.

"Our people have been watching the situation and don't feel there is any emergency that warrants federal interference at this time," Reagan said.

"This is not a major threat to the banking system," he added.

The president said that insurance is still available to qualified institutions, and he complimented the Federal Reserve for agreeing to loan funds needed to help the institutions reopen.

"There isn't anything else for the federal government to do," Reagan said.

Savings One Association in Mansfield opened for limited withdrawals without state authorization Wednesday and about 60 people were waiting outside its office when it unlocked its doors today. Southern Ohio Savings Association of St. Bernard and the Federal State Bank of Lockland also opened without authorization.

"We are encouraged by the experience at Century," Usher said. "There seemed to be more newsmen than customers there, and many of the customers were making deposits. We think the confidence of depositors is a signal that we have come up with a strong solution to this problem."

Meanwhile, Ohio Attorney General Anthony Celebrezze appointed Lawrence A. Kane Jr., a Cincinnati lawyer, as special prosecutor to investigate the collapse of the Cincinnati-based Home State Savings Bank, which triggered a run on deposits at other state-chartered institutions last week. Kane is a Republican.

Home State is owned by Marvin L. Warner, a former U.S. ambassador to Switzerland and Celeste's chief fund raiser.

Celeste, a Democrat, closed 71 S&Ls for a "bank holiday" Friday to stop the run, and officials have been uneasy since about what would happen once they reopened. The first indication came Monday when Columbia Savings and Loan of Cincinnati, which had been put under federal insurance protection, opened without incident.

Under an emergency law enacted Wednesday, thrifts can open for full service if they apply for federal insurance protection, if they are owned or have agreed to merge with a company already federally insured or if they can convince state regulators that deposits are otherwise fully protected.

Other institutions can reopen for limited service, but customers will be allowed to withdraw no more than $750. They also can make deposits. Twenty-four institutions have applied for federal insurance coverage, according to the governor's office.

Cursory audits of the 70 closed institutions last week indicated that as many as 25 to 30 may be too weak to reopen. Another 20 or 25 are salvageable but need help, while the remaining 25 or 30 probably can qualify for federal insurance, federal officials said. Federal insurance requires that an institution have net worth in excess of 5 percent of its assets.

All previously were protected under a private fund, but losses at Home State threatened to exhaust the $136 million in the fund.

Century was allowed to reopen because it has applied for federal insurance and is owned by State Savings Bank, a large federally insured institution. About 30 depositors had closed their accounts at a Toledo branch by midday, compared with one or two on a normal day.

But there was no sign of panic at a Century branch in the Columbus suburb of Upper Arlington, where smiling top executives from State Savings wearing red carnations in their lapels greeted customers.

"I need the money, but I'm only going to take out a little," said Sarah Bach, the first customer in line this morning.

One real estate developer came in to withdraw $76,000, but changed his mind after Allan B. McFarland, president of State Savings, embraced him. "Everyone is a little nervous," said the developer, who asked not to be named. "I was going to move my money somewhere else, but I've known Allan McFarland for 25 years, and he convinced me it was safe here. He did a number on me."