NAIROBI (Reuters) - A majority of Kenyans would endorse a proposed new constitution in a referendum although most are unhappy about one thing or another in the draft charter, a poll published on Saturday showed.

Kenyans have been calling for a new constitution since the 1990s to replace one dating back to 1963. Guarantees of a new charter were central to a power-sharing deal in 2008 that ended weeks of violence that killed about 1,300 people after a disputed poll.

Parliament voted unanimously in favour of the draft this month but some legislators are now asking Kenyans to vote against it when it comes to the referendum to be held in late July or early August.

A total of 64 percent said they would vote Yes if a referendum on the constitution were held now and 17 percent said they were against it. The remainder were undecided, the survey by pollster Synovate said.

"Kenyans are very eager to have a new constitution," said George Waititu, Synovate's managing director. "It is one of the tools they are looking forward to, to have the country governed better."

The new legal framework would curtail sweeping presidential powers and strengthen civil liberties.

The poll showed 68 percent of potential voters were unsatisfied with at least one issue in the proposed charter.

"We are seeing a high degree of tolerance. 68 percent of potential voters have something they don't like but the majority are supporting the draft nevertheless," Waititu told reporters.

And 91 percent of the 2,003 Kenyans surveyed said it was absolutely or quite important that the country had a new constitution although 45 percent of them said they knew very little or nothing of what the draft contained.

A total of 37 percent said they had personally formed their own opinion of the new constitution; 21 percent said they had been influenced by politicians and 19 percent had been swayed by religious leaders.

Some politicians are backing a No vote, angry at the failure to devolve power to the regions and plans to cap private land holdings.

Some Christian church leaders are also spearheading a No campaign after an amendment to abolish abortion on medical grounds failed, while Islamic courts dealing with divorce and inheritance were left enshrined in the constitution.