Filed at 3:59 p.m. ET

NEW YORK (Reuters) - U.S. Secretary of State Hillary Clinton urged Turkey and Armenia Monday to carry out their plans to normalise ties soon during separate meetings with their foreign ministers.

Her comments appeared to reflect uncertainty about whether the countries will stick to their plan to sign a pact restoring diplomatic ties and reopening their border by mid-October.

Signing the deal would help to end almost a century of hostility stemming from the World War One killings of Armenians by Ottoman Turks.

Turkey rejects Armenian claims the killings, a defining element of Armenian national identity, amount to genocide, and says many people were killed on both sides of the conflict.

"I want to reiterate our very strong support for the normalization process that is going on between Armenia and Turkey, which we have long said should take place without preconditions and within a reasonable timeframe," Clinton told reporters as she sat down with Armenian Foreign Minister Edward Nalbandian on the sidelines of the U.N. General Assembly.

She later met Turkish Foreign Ahmet Davutoglu.

A U.S. official said Clinton does not want the signing to be disrupted by Armenian nationalist demands that Turkey acknowledge the 1915 killings as genocide or by demands by some Turks for a resolution of the Nagorno-Karabakh dispute.

Turkey closed its frontier with Armenia in 1993 in solidarity with its Muslim ally Azerbaijan during the war in Nagorno-Karabakh, where ethnic Armenians threw off Azeri rule with the backing of Armenia.

Armenia and Turkey on August 31 said they would sign accords within six weeks to restore ties and reopen their border.

(Reporting by Arshad Mohammed, editing by Anthony Boadle)