SINGAPORE (AP) _ The government rejected an American reporter's application to work in this island-republic and denied permission to a second journalist seeking to extend his employment pass.

No reason was given for the decisions, and officials refused to elaborate today. Both reporters work for the AP-Dow Jones News Service.

The employment pass, required by foreigners employed in Singapore, was denied Matthew K. Geiger, a U.S. citizen who was to have been assigned from New York.

A letter signed on behalf of the Controller of Information, dated Nov. 18 and received Thursday by AP-Dow Jones in Singapore said, ''I regret that the application is not approved.''

Geiger applied for the pass on Sept. 28 to replace Simon Elegant as regional correspondent for the financial news service.

Elegant's request for a two-month extension of his employment pass was denied in October, and he left Singapore after being based here three years.

''We are puzzled by this action and will be seeking further information about why it was taken,'' AP-Dow Jones Managing Editor James Furlong said in New York.

AP-Dow Jones is jointly owned by The Associated Press and Dow Jones and Co. Dow Jones also is majority owner of The Asian Wall Street Journal and sole owner of the Far Eastern Economic Review.

Singapore has refused to let the Asian Journal base a reporter in the country since mid-1988 and has refused to let the Review base a reporter here since mid-1987.

Since February 1987, Singapore has restricted circulation of the Asian Journal to 400 copies a day from about 5,000 previously.

The Review's circulation was restricted to 500 copies a week in December 1987, down from about 9,000.

Both Hong Kong-based organizations had their circulations slashed under a 1986 amendment to the Newspapers and Printing Presses Act that enables the government to restrict the sale and distribution of a publication that is deemed to be engaging in domestic politics.

Both denied that any articles appearing in their pages constituted such interference.