The broader Dow Jones Insurance Index, which includes Travelers and peers such as Chubb Corp. and AIG, fell 3 percent.

Travelers had previously been able to hold on to customers and keep insurance pricing consistent across its businesses to offset perennially low interest rates.

But increasing competition has resulted in the company writing fewer policies, forcing it to resort to rate cuts.

The personal auto insurance business reported a 7 percent fall in written premiums during the second quarter as the company's strategy to increase prices hurt income from premiums. The business contributed about 14 percent to the total premiums written during the quarter.

In a slide presentation for analysts, the company noted that the rate at which it raised premiums across businesses fell from that in the first quarter.

“Travelers reported a deceleration in its Business Insurance pricing in 2Q13 compared to 1Q13. While still positive, the market is taking it as the sign that the property and casualty rate improvements may have peaked,” BMO Capital Markets analyst Charles Sebaski said in an email to Reuters.

The company, however, said renewal rates at its business insurance unit were consistent with those in recent quarters.

“Given the environment of low interest rates and volatile weather patterns, we will continue to seek higher margins,” Chief Executive Jay Fishman said in a statement.

Travelers reported a strong second-quarter profit that blew past estimates for the fourth straight quarter, boosted by higher rates and lower claim payouts.

The company's operating earnings of $2.13 per share was well above the average analyst estimate of $1.60, according to Thomson Reuters.

Travelers' earnings often differ substantially from Wall Street consensus as the company does not give forecasts.

Analysts' estimates for the insurer's per-share operating earnings ranged from $1.26 to $1.86 a share, according to Thomson Reuters StarMine.

“This appears to be a quality beat, not dependent on the favorable prior-period development,” BMO's Sebaski said.

The company said it would cut 450 jobs and take a related restructuring charge of about $16 million, of which $10 million would be incurred in the current quarter.

The cost cutting will result in cumulative savings of $140 million by 2015, Chief Operating Officer Brian MacLean said on a conference call with analysts.

The company's combined ratio, the percentage of premium revenue an insurer has to pay out in claims, fell to 94.3 percent from 100.5 percent last year.

A combined ratio under 100 indicates an underwriting profit.

Travelers last month said it would pay about $1.1 billion to buy Dominion of Canada General Insurance Co to boost its presence in the Canadian market.

Travelers shares were trading down 3.6 percent at $82.33 on the New York Stock Exchange on Tuesday.