(Adds quotes from new president of assembly paras 12-13) By David Ljunggren QUEBEC CITY, Nov 17 (Reuters) - The head of the NATO military alliance urged member nations on Friday to drop the restrictions they impose on their troops in Afghanistan, saying this was hampering the ability to fight Taliban militants. NATO currently has around 31,000 soldiers in Afghanistan but some member nations have placed so-called caveats on what their troops can do. Some are not allowed to operate at night and others have been banned from fighting altogether. The caveats have upset the United States, Britain and Canada, who complain their soldiers are doing most of the fighting against the Taliban in southern Afghanistan. NATO Secretary-General Jaap de Hoop Scheffer asked a Quebec City meeting of parliamentarians from the 26 member nations to persuade their governments to lift the restrictions. "An operational commander can have lots of trouble if too many caveats exist in the written or unwritten form. Too many caveats limit the possibilities a commander has to use his forces," he said by video link from NATO's Brussels headquarters. "My strong plea to governments and also my strong plea to you parliamentarians would be -- please help us in lifting those caveats as much as possible ... you have an important role to play here, because really in Afghanistan it is a problem." De Hoop Scheffer said he realized that in some member states troop deployments needed to be approved by parliaments and that the caveats had been demanded by legislators. But he said the restrictions could also be seen as divisive. Canadian Defence Minister Gordon O'Connor told the meeting that "all NATO allies must prove themselves by sharing the burden in all regions of Afghanistan" equally, and said Ottawa expected the caveats to be removed. "We need to ensure that troops can be deployed in areas where they are needed the most," he said. Canada has 2,500 soldiers in southern Afghanistan, with more than 40 killed since 2002, most of them in the last few months. Recent polls have mostly shown that a majority of Canadians oppose the mission. O'Connor said the government had not done a good enough job of selling the mission's merits, saying "we haven't been as aggressive in this as we should have". Bert Koenders, a Dutch legislator elected the new head of the NATO parliamentary assembly on Friday, told a news conference it was "very difficult if some countries are consistently doing less in difficult situations than others". NATO leaders will hold a summit in the Latvian capital Riga at the end of this month and Koenders said he hoped peer pressure could help persuade reluctant countries to do more. De Hoop Scheffer did not address another major problem NATO is facing, that of persuading member nations to send more soldiers to Afghanistan. NATO's top commander said in late October that the alliance did not have enough soldiers in Afghanistan to secure a victory over Taliban fighters in the coming months. In the short-term, NATO is looking for another 1,500 soldiers, and the issue is set to dominate the Riga summit. British legislator Bruce George, a member of the ruling Labour Party, told reporters at the Quebec City meeting earlier this week it was "a bloody disgrace" that NATO members were not stepping up to provide more troops.