By David Alexander and Andrea Shalal WASHINGTON (Reuters) - The Pentagon on Tuesday proposed a $582.7 billion defense budget that emphasizes emerging threats from Russia, China and Islamic State rebels, but the plan is already under fire from Republican lawmakers who charge it short-changes the U.S. military. President Barack Obama's last budget would boost spending on the war against Islamic State militants to $7.5 billion during the 2017 fiscal year, a 50 percent jump over the $5 billion approved this year. Some $200 million of that would go to fight militants in north and west Africa. The proposal also would quadruple funds to counter Russian pressure in Europe, including its seizure of Ukraine's Crimean peninsula and repeated strategic bomber flights near NATO air space. Spending to boost U.S. military presence and training in Europe would rise to $3.4 billion from $800 million this year. The budget heralds a strategic shift as Washington looks beyond the wars in Iraq and Afghanistan that have dominated U.S. foreign policy over the past 15 years and enters a new period of great power competition from Russia and China as well as threats from smaller rivals like Iran and North Korea, officials said. "This budget marks a major inflection point for the Department of Defense," Defense Secretary Ash Carter said in a statement. "Even as we fight today's fights, we must also be prepared for the fights that might come in 10, 20 or 30 years." Overall, the administration is seeking a Pentagon base budget of $523.9 billion for the fiscal year beginning Oct. 1, plus $58.8 billion for war funding and overseas operations. The base budget is about $2.5 billion more than this year's while war spending remains relatively flat, officials said. The spending proposal is in line with a congressional budget deal last year that set Pentagon funding guidelines for 2016 and 2017. But Republican lawmakers have criticized the war funding plan, saying the $59 billion figure in the budget deal was a floor, not a ceiling, and the president should have sought more. "This request is inadequate to address the national security threats we face and the growing demands they impose on our men and women in uniform," Senator John McCain, chairman of the Senate Armed Services Committee, said in a statement. Congressman Mac Thornberry, chairman of the House of Representatives Armed Services Committee, accused administration of continuing "to play budgetary games with our country's security." McCain said by seeking the minimum level of war funding agreed in last year's budget deal, the president had left the Pentagon with at least $17 billion less than it estimated it would need for 2017 in last year's budget. To make up the shortfall in planned spending, the Pentagon cut more than $5 billion by adjusting its assumptions about expected fuel costs and inflation levels, Pentagon Comptroller Mike McCord said. It also reduced procurement to $112.1 billion, a drop of $11.2 billion, or 6 percent, from this year. The reductions would come mainly from cuts in planned aircraft purchases, including five fewer F-35 Joint Strike Fighters and a reduction in several types of Army helicopters, budget documents show. While cutting procurement, the Pentagon proposed increasing spending on research and development by 4 percent, to $71.8 billion, as it looks to develop new military technologies that can give it an edge over rival forces. The budget would continue to shrink the size of the U.S. Army following the Iraq and Afghan wars, dropping to 460,000 soldiers in 2017 from the current 475,000. The department plans to further reduce the force to 450,000 in the coming years. (Reporting by David Alexander, Andrea Shalal and Yeganeh Torbati; Editing by Chizu Nomiyama and James Dalgleish)