By Andrew Hammond

BAGHDAD, Nov 20 (Reuters) - A growing number of Iraqis think occupying U.S. troops should stay in Iraq until the security situation improves, research published this month has shown.

In a survey carried out by the respected Psychological Research Centre of Baghdad University, 71.5 percent of Iraqis think the U.S. occupation is necessary at least for a while, compared to 42 percent in a survey by the centre in June.

"This shows an acceptance of the foreign presence as a temporary solution because of the fear, confusion and absence of law and order following the collapse of the old regime," the report said.

U.S. President George W. Bush said on Thursday more troops could be sent to Iraq if necessary to secure the country. "We will finish the job we have begun," he said in London.

The study obtained by Reuters on Thursday also showed 63.2 percent approved of the Governing Council, appointed by the U.S. occupying authorities in July, as a first step towards stability and a new Iraq. Only 36.8 percent said the Council merely reinforced the occupation.

The research was carried out over a sample of 1,000 people from different sectors of the population all over the country of about 26 million people, which has seen security deteriorate amid a mounting insurgency against U.S. forces.

But the study, which included Kurdish areas in the north, showed more Iraqis now favoured a monarchy along Islamic lines.

Of 53.3 percent of respondents who favoured a monarchy from a series of choices, about 70 percent said they preferred it to be "Islamic". Of the 46.7 percent who favoured a republic, about 75 percent said it should have an Islamic flavour.

Only 20 percent of respondents favoured a monarchy in the earlier study and only eight percent chose "Islamic government".

A royalist party has been set up by a member of the British-backed Hashemite monarchy that ruled Iraq until a 1958 coup, one of dozens of new political parties.

Islamic groups now dominate Iraq's political arena after three decades of secular Baath Party rule ended this year.

"This is an indicator of the importance that citizens hope Islamic ideology will have in their future government," the report said, adding that the monarchy was seen as untainted by the repression of the Baathist era.

Harith Hassan, head of the research team, said he would send the results to U.S. administrator Paul Bremer. Both studies have been presented to the Governing Council, but with no response.

"I told them we were happy to provide them with any kind of research, but they don't seem to care," he told Reuters.

The November report showed 52.6 percent of Iraqis rejected the idea of federalism, which the Council has said will be a guiding principle of Iraq's new political system.

"People don't know what federalism means. People think it's about dividing the country," Hassan said.