The median sale price for the first quarter was $775,000, unchanged from the same period in 2011, according to a report from Streeteasy.com that will be released on Tuesday. Reports from New York City’s largest brokerages also indicate relatively steady pricing, with one showing the median dropping by 1 percent and others an increase of 4 percent to 6 percent.

The average price rose, with Brown Harris Stevens and Halstead Property showing a 9 percent increase over last year to $1.48 million. That number, however, was skewed by strong sales in the luxury market, including an $88 million penthouse at 15 Central Park West.

Hall F. Willkie, the president of Brown Harris Stevens, which represented the buyer and the seller in the $88 million deal, said the sale “had an immediate effect on comparable properties, but it also had an impact on the overall market in terms of confidence.”

“It provided an emotional lift across the board,” he continued.

The reports reflect deals that went into contract late last year and that closed through the end of March, but brokers said many of the sales that had gone into contract in recent weeks involved multiple bids above the asking price.

Bidding wars returned to the market last year, but Halstead’s president, Diane M. Ramirez, said that until recently most of the bidding merely drove the sale price close to the list price. “It’s definitely a good sign that things are now starting to go over ask,” she said.

That trend has been seen at all levels of the market, Ms. Ramirez added, but typically only when an apartment is in good condition, in a good location and priced well. She said sellers who listed their homes above the market rate to add a cushion for negotiation were making a mistake.

“If you’re not priced correctly, everyone will walk right by you,” she said.

Pamela Liebman, the chief executive of the Corcoran Group, said that after two years of stable pricing, “I think we’ve finally gone beyond steady and are starting to get into a real uptick.” Corcoran’s report showed the strongest numbers, with the median rising 6 percent to $809,000.

Ms. Liebman said luxury sales buoyed the market. She mentioned two listings that recently drew multiple bids and went into contract within a few weeks of coming to market: a $24.5 million duplex on the Upper East Side and a $7.95 million West Village town house. “I think buyers have gotten the message that if you’re ready to buy, be prepared to bid aggressively and to sign quickly,” she said.

A $24 million apartment owned by the reclusive heiress Huguette Clark, who died last year, also went into contract within a week of being listed last month. Mr. Willkie, whose agency represents the Clark estate, would not say if the bidding pushed the price for the 12th-floor apartment over the asking price. Mrs. Clark’s two other apartments in the same Fifth Avenue building, priced at $12 million and $19 million, are still available.

On the low end, Jonathan J. Miller, the president of the appraisal firm Miller Samuel and the author of Elliman’s report, said there was a surge in sales of studios and one-bedrooms. The market share for those small apartments rose to 56.2 percent, the highest percentage since late 2009 and up from 49.4 percent last year.

“The entry level came back strong,” said Dottie Herman, the chief executive of Prudential Douglas Elliman, “because people know that rents are only going to go up, and at the same time they’re worried about interest rates spiking. All those things make it more appealing to buy right now.”