ALMATY (Reuters) - Uzbekistan's parliament named Prime Minister Shavkat Mirziyoyev as interim president on Thursday in succession to the late President Islam Karimov, saying stability and law and order had to be maintained in the populous Central Asian state.

Mirziyoyev, 59, secured the top job when the man who should have become transitional leader under the constitution bowed out in his favor, saying he had long experience in office and enjoyed the respect of people.

The authoritarian Karimov died of a stroke last week aged 78 after ruling the resource-rich country for 27 years.

Under the Uzbek constitution, a presidential election must now be held within three months, and Mirziyoyev, who was the official mourner-in-chief at Karimov's funeral and met Russian President Vladimir Putin this week, is widely expected to be elected.

Russia, the United States and China vie for influence in Uzbekistan, a country of 32 million bordering Afghanistan.

Central Asia pundits say they do not expect any drastic policy changes under Mirziyoyev, a former regional governor valued by Karimov as a competent manager.

With his appointment as acting head of state, Mirziyoyev leapfrogged the little-known Senate chairman Nigmatilla Yuldashev, who under the constitution should have led the country during the transition period.

Yuldashev turned down the role and instead asked to for Mirziyoyev to be instated as acting president, taking into account "his long experience of work in executive positions and respect among the people", the parliament said in a statement.

Parliament supported Yuldashev's motion, stressing the "need to preserve stability, public security, law and order and effectively resolve political and economic issues".

Karimov cast his country as a bulwark against militant Islam but drew Western criticism for suppressing political dissent. Human rights groups say there are hundreds of political and religious prisoners in local jails and say torture is practiced.

In contrast to the West, Putin said during his visit to Tashkent this week he hoped the new Uzbek leader would continue Karimov's work, putting a stamp on Moscow's claim to be the former Soviet republic's closest ally.

(Reporting by Dmitry Solovyov; Editing by Richard Balmforth)