Insurance rates will likely continue to rise this year, but some policyholders with good loss records can obtain flat renewals as insurers sometimes offer expiring rates to win new business, Brown & Brown Inc.’s top executive said Tuesday.

“We’re starting to see a gap between renewal increases and new business pricing,” said J. Powell Brown, president and CEO of the brokerage.

Most policyholders will still likely see higher rates this year, although there may be some moderation in the second half, he said.

Mr. Brown was speaking on the brokerage’s conference call with analysts discussing Brown & Brown’s first-quarter results, which saw strong revenue growth.

Brown & Brown reported two acquisitions during the quarter and has a strong pipeline of potential deals, Mr. Brown said. He declined to comment on the possibility of buying any business sold by Aon PLC to secure its purchase of Willis Towers Watson PLC but did not rule out the possibility.

Brown & Brown reported first-quarter revenue of $815.3 million, up 16.7% from the same period last year and up 9.8% on an organic basis. Organic revenue, which excludes acquisitions and various other changes, increased 9.8% in its retail segment, 13% in programs, 6.8% in wholesale, and 5.7% in services.

Quarterly profit increased to $199.7 million, up 31% over the year-earlier period.

Premium rate increases in the first quarter were similar to the last few quarters, Mr. Brown said.

Admitted market rates were up 3% to 7% across most lines, though some lines saw much larger increases. Commercial auto rates rose 10% or more; excess and surplus lines rates were up 10% to 20%, with coastal property up 15% to 25%; and professional liability was up 10% to 25%.

Workers compensation rates continued to decline but are getting close to flat.

“Overall, the market is becoming more competitive in sections or areas and we are starting to see carriers willing to bind coverage at the expiring rate for new business but that same carrier would like to get increases for their renewals,” Mr. Brown said.

The flat renewals for new business are occurring most frequently on middle-market and upper middle-market accounts in the Northeast and Midwest, he said.

The brokerage’s two acquisitions in the quarter, including the purchase of Cork, Ireland-based O’Leary Insurances Ltd., added about $33 million in revenue.

Mr. Brown said he expects Aon’s purchase of Willis Towers Watson to be completed but declined to comment on whether Brown & Brown would be interested in buying any of the business that might be sold by the brokers to secure regulatory approval of the deal.

“We are always interested in looking at good businesses that we believe could fit culturally and make sense financially,” he said. “We don’t like the terms never or always because they are a little extreme.”