Russia has halted all military cooperation with NATO, the Western alliance said Thursday, in the latest sign of East-West tension over the invasion of Georgia. Alliance spokeswoman Carmen Romero said NATO had received notification through military channels that Russia's Defense Ministry had taken a decision "to halt international military cooperation events between Russia and NATO countries until further instructions." She said NATO "takes note" of the decision but had no further reaction. On Tuesday, NATO foreign ministers said they would make further ties with Russia dependent on Moscow making good on a pledge to pull its troops back to pre-conflict positions in Georgia. However, they stopped short of calling an immediate halt to all cooperation. Under a 2002 agreement that set up the NATO-Russia Council, the former Cold War foes began several cooperation projects. They include sharing expertise to combat heroin trafficking out of Afghanistan, developing battlefield anti-missile technology, joint exercises and help with rescue at sea. Romero said she was unaware of any specific events under the cooperation agreement scheduled before early September. NATO itself decided last week to suspend plans for a Russian warship to join NATO counterterrorism patrols in the Mediterranean Sea, deciding it was inappropriate in the wake for the eruption of fighting in Georgia. Meanwhile France's foreign minister said Thursday that two small columns of Russian troops were leaving Georgia, in what he called an encouraging sign of a much-awaited pullout. "Some encouraging signs, even if they are insufficient, were made yesterday and today," including the departure of the columns, Bernard Kouchner told reporters in Paris. He did not say where the troops were or where they were going. He said that after previous hopes of a pullout were dashed, "this time it appears that there is at least the beginning of a fulfillment." But even as Kouchner praised the progress, Russian forces dug deeper into their positions at the entrance to Georgia's main Black Sea port city of Poti, excavating trenches and setting up mortars facing the city. Several armored personnel carriers and troop trucks blocked the bridge that is the only land entrance to Poti and another group of APCs and trucks were positioned in a nearby wooded area. Although Russian President Dmitry Medvedev has promised that his forces would pull back by Friday, Russian troops appear to be settling in for a long presence, raising concern about whether Moscow is aiming for a lengthy occupation of its small, pro-Western neighbor. Nonetheless, a top Russian general said troops were moving out in accordance with the agreement. "The pullback of Russian forces is taking place at such a tempo that by the end of August 22 they will be in the zones of responsibility of Russian peacekeepers," Col.-Gen. Anatoly Nogovitsyn, the deputy head of the general staff, said at a briefing Thursday in Moscow. Georgian President Mikhail Saakashvili told The Associated Press that Russia was seizing strategic spots in Georgia even as it thinned out troops elsewhere. He called the Russian moves "some kind of deception game." "[The Russians] are making fun of the world," he declared. An EU-sponsored cease-fire says both Russian and Georgian forces must move back to positions they held before fighting broke out August 7 in Georgia's separatist republic of South Ossetia, which has close ties to Russia. The agreement also says Russian forces can work in a so-called "security zone" that extends 7 kilometers into Georgia from South Ossetia. Russian forces are also allowed a presence on Georgian territory in a security zone along the border with Abkhazia, another separatist Georgian region, under a 1994 UN-approved agreement that ended a war there. But Poti is 30 kilometers south of Abkhazia and lies well outside the security zone - and it's also at least 150 kilometers west of the nearest point in South Ossetia. Russian tanks, trucks and troops meanwhile continued to hold positions Thursday around the strategically key city of Gori and in Igoeti, about 50 kilometers west of the Georgian capital of Tbilisi. Both are along Georgia's main east-west highway. Georgia said Russian soldiers destroyed military facilities Wednesday in Osiauri, but the claim could not be confirmed. Several thousand people rallied Thursday in the Abkhazian capital Sukhumi to demand the region be recognized as independent and a similar rally was expected in South Ossetian capital Tskhinvali later in the day. Russian officials, including Medvedev, have indicated Moscow will recognize the regions as independent. Despite the EU peace accord, Nogovitsyn said Georgia has "no moral right" to return its soldiers to South Ossetia, where they had held some land as part of a peacekeeping mission. He said Russia will build 18 checkpoints in the security cordon around the province. Western leaders have stressed that Georgia must retain its current borders. The war in a small country straining to escape Moscow's influence has sent tensions between Moscow and the West to some of their highest levels since the 1991 breakup of the Soviet Union.