Mayor Bill de Blasio has asked New York City commissioners to look for ways to cut costs in a gesture of fiscal moderation prompted by worries over the rocky world economy, drawing cautious praise from budget watchdogs.

The city budget director, Dean Fuleihan, told agency leaders in an email on Monday that they must find ways to trim expenses but did not specify how much.

“It’s a step forward,” said Carol Kellermann, president of the Citizens Budget Commission, a nonpartisan fiscal monitoring group, which had been pushing the mayor to institute a regular cost-cutting measure similar to those used by his predecessors. “It says, ‘Every agency, please come up with some savings.’”

But she criticized the move for its lack of specific goals.

Mr. Fuleihan said in the email, “We are preparing this year’s executive budget in the midst of economic and fiscal uncertainty,” citing volatile stock markets and slowing economies around the world. As a result, he wrote, agencies would be required to “identify significant new savings.”