* Putin says NATO should stay in Afghanistan longer
* Russia worried 2014 pullout may destabilise region
* Russia makes Ulyanovsk airport available to NATO
By Gleb Bryanski
ULYANOVSK, Russia, Aug 1 (Reuters) - NATO forces should stay in Afghanistan until they have finished their job to ensure stability, Russian President Vladimir Putin said on Wednesday, criticising the planned withdrawal of most combat troops by 2014.
Putin reiterated Kremlin concerns that the pull-out of the U.S.-led alliance, due to start next year, will leave the Central Asian region south of Russia vulnerable to militant violence and drug trafficking.
"It is regrettable that many participants in this operation are thinking about how to pull out of there. They took up this burden and should carry it to the end," Putin said at a meeting with paratroopers in the Russian city of Ulyanovsk.
"If there is no order in Afghanistan it will not be calm on our southern borders. The current (Afghan) leadership will have difficulties keeping the situation under control. NATO member states are present there, and are performing this function," he said.
"We need to help them (NATO). We should not be fighting there again. Let them sit there and fight."
The Soviet Union fought a disastrous war in Afghanistan in the 1980s and Russia ruled out sending troops to aid the U.S.-led invasion after the Sept. 11, 2001 attacks.
But Moscow has supported the NATO operation by allowing transit across its territory.
It expanded that support with an agreement that took effect on Wednesday allowing the alliance to use a transit hub in Ulyanovsk to send non-lethal supplies in and out of Afghanistan using the Russian rail network and air transport.
Supply routes are particularly important for the NATO operation in Afghanistan and the planned pull-out.
Removing a major headache for the alliance, Pakistan re-opened NATO transit lines via its territory in July after months of closure over NATO air strike that killed 24 Pakistani soldiers.
Putin said the transit hub agreement, which has drawn criticism from Communists and others saying Russia is allowing an enemy on its territory, in fact benefited Russia - which is otherwise often at loggerheads with the alliance.
"It corresponds to our national interests. On many other issues we have disagreements. We have different approaches, opinions." Putin said, reiterating his description of NATO as a "throwback to the past, to the times of the Cold War".
"We will cooperate with them on other fields, fighting piracy on the sea, international terrorism, organised crime. But we will always follow our national interests," the former KGB spy said.