American International Group Inc. said four of its 15 most-senior executives are departing, continuing an effort by Chief Executive Peter Hancock to realign duties and cut costs as the insurer faces pressure from big investors to improve profitability.

The departures will shrink an advisory committee of high-ranking executives that Mr. Hancock formed shortly after taking over as CEO in September 2014. It will become a 10-member team, down from 15.

The shake-up is part of a broader plan, unveiled last month, to cut up to 23% of AIG’s senior management, or as many as 320 positions. Duties of the four departing executives will largely be distributed to executives who are remaining. A fifth executive leaving the advisory committee will stay at the company.

The revamping is aimed at making AIG less complex, more efficient and able to make decisions faster, AIG said in a news release.

Since late October, billionaire investors Carl Icahn and John Paulson made public separate proposals to break up the insurer into three parts.

The investors say such a breakup would reduce the company’s regulatory burden and allow it to return more capital to stockholders through share buybacks. They are also pushing for stepped-up cost-cutting to bring the company’s financial results more in line with better-performing peers.

Mr. Hancock has responded publicly that management and the board have reviewed the idea of breaking up the insurer and concluded that such a move doesn’t make financial sense. He has said he wants the company to continue with strategic priorities he has had in place for months, which include further narrowing of AIG’s operations with some divestitures.

In the news release Thursday, Mr. Hancock said that AIG is “moving forward with a continued sense of urgency” on top priorities, including the existing goals of narrowing its focus on the most-profitable areas, “growing through innovation,” and returning excess capital to shareholders.

Two of the four departing executives have key roles running AIG’s core property-casualty insurance operations, where the company has struggled to match the strong financial performance of peers such as Travelers Cos. and ACE Ltd. A third is Chief Financial Officer David Herzog.

Mr. Herzog, 56 years old, isn’t leaving as a result of disagreement over financial matters, company spokesman Jon Diat said. “David did not have a conflict with Peter,” he said, but instead Mr. Herzog is retiring. He will continue as financial chief through the filing of the company’s 2015 annual statements in early 2016. Mr. Herzog will be succeeded by Sid Sankaran, 38, currently the chief risk officer. Mr. Herzog declined to comment.

Many of the changes the company has put in place to improve the unit have yet to pay off, but Mr. Hancock believes they have positioned the company for better results, people familiar with the matter said.

Those changes include the installation of information-technology infrastructure that will better automate some functions and the naming of a new chief underwriting officer who has extensive experience in data analysis. In addition to boosting efficiency, such changes are aimed at incorporating more use of data analytics into evaluation of risks in particular clients or entities to be insured.

AIG has said it would give an update of its strategy in advance of its fourth-quarter earnings report in early February.

AIG, which received a nearly $185 billion government bailout during the financial crisis, is one of three insurers that have been designated “systemically important” by a panel of federal regulators. The designation subjects it to yet-to-be-determined but potentially onerous capital rules.

In announcing the 23% reduction in the ranks of senior managers last month, Mr. Hancock said the company needs “fewer generals on the field,” having shrunk dramatically in size over the past several years through divestitures to fully repay its bailout.

Besides Mr. Herzog, those departing the company will be John Q. Doyle, 52, chief executive of the company’s big commercial-insurance operations; R. Eric Martinez Jr., 48, who is head of global claims and operations; and Jose A. Hernandez, who is CEO of Asia Pacific region.

Among those gaining added responsibilities will be Robert Schimek, who currently heads the company’s Americas region. He will take the title of CEO of commercial operations and assume responsibility for the commercial claims organization, according to the release. Kevin Hogan, currently CEO of consumer insurance operations, will add claims responsibilities, as well.

Also gaining broader duties will be Seraina Maag, currently president and CEO overseeing a part of AIG’s international operations, AIG said.

Chief Science Officer Murli Buluswar will leave the executive-leadership team but not the company. Rather than report directly to Mr. Hancock as he does now, he will report to Chief Investment Officer Douglas A. Dachille.

Write to Leslie Scism at leslie.scism@wsj.com