President Donald Trump called Russian President Vladimir Putin to congratulate him on his re-election, drawing bruising criticism from members of his own party, including a leading senator who scorned the election as a 'sham.' Trump also said he and Putin might meet 'in the not too distant future' to discuss the arms race and other matters. What they didn't discuss on Tuesday was noteworthy as well: Trump did not raise Russia's meddling in the U.S. elections or its suspected involvement in the recent poisoning of a former spy in Britain. Trump's aides had warned him in an all-caps note to refrain from congratulating Putin, The Washington Post reported. It said aides included a section in his briefing materials stating: 'DO NOT CONGRATULATE.' It was unclear whether Trump, who prefers oral briefings, read the talking points prepared by his national security team before the call. Criticism came quickly. 'An American president does not lead the free world by congratulating dictators on winning sham elections,' said Sen. John McCain, R-Ariz., who chairs the Senate Armed Services Committee and has pressed the Trump administration to respond aggressively to Russia's interference in the U.S. presidential election. Sen. Jeff Flake of Arizona, a frequent Trump critic, called the president's call 'odd.' Senate Majority Leader Mitch McConnell said Trump 'can call whomever he chooses' but noted that calling Putin 'wouldn't have been high on my list.' At the State Department, spokeswoman Heather Nauert said it was 'no surprise' that Putin was re-elected, commenting that some people were paid to turn out to vote and opposition leaders were intimidated or jailed. She also cited a preliminary report by the Organization for Security and Cooperation in Europe that said Russia's election took place in an overly controlled environment that lacked an even playing field for all contenders. Her comments were notably tougher on Russia than those coming from the White House. White House press secretary Sarah Huckabee Sanders defended Trump's call, and noted that President Barack Obama made a similar call at the time of Putin's last electoral victory. 'We don't get to dictate how other countries operate,' Sanders said. The action and reaction fit a Trump White House pattern of declining to chide authoritarian regimes for undemocratic practices. Trump himself has long been reluctant to publicly criticize Putin. He said that during their hoped-for meeting the two men would likely discuss Ukraine, Syria and North Korea, among other things. 'I suspect that we'll probably be meeting in the not too distant future to discuss the arms race, to discuss the arms race, which is getting out of control, but we will never allow anybody to have anything even close to what we have,' Trump said. Russia has received global condemnation after Britain blamed Moscow for the recent nerve agent attack that sickened Sergei Skripal and his daughter. Russia has denied the accusation. Trump's call came at a period of heightened tensions between the two nations after the White House imposed sanctions on Russia for its interference in the 2016 U.S. election and other 'malicious cyberattacks.' Sanders insisted that the administration has scolded Putin at the appropriate times. 'We've been very clear in the actions that we've taken that we're going to be tough on Russia, particularly when it comes to areas that we feel where they've stepped out of place.' The Kremlin said in a statement that Trump and Putin spoke about a need to 'coordinate efforts to limit the arms race' and for closer cooperation on strategic stability and counterterrorism. 'Special attention was given to considering the issue of a possible bilateral summit,' the Kremlin statement said. In addition, the two presidents expressed satisfaction with the apparent easing of tensions over North Korea's weapons program, according to the Kremlin. No details were released about the timing or location of a possible meeting, which would be their third since Trump took office in January 2017. They met on the sidelines of an international summit in Germany last summer and again more informally at another gathering of world leaders in Vietnam in November. The presidents 'agreed to develop further bilateral contacts, taking into account changes in the U.S. State Department,' the Kremlin statement said in a reference to Trump's decision to replace Secretary of State Rex Tillerson with CIA Director Mike Pompeo. Russia has repeatedly said it hoped for better ties with the U.S. under Trump. Putin received calls from a number of other foreign leaders, including French President Emmanuel Macron, Chinese President Xi Jinping, Japanese Prime Minister Shinzo Abe and Indian Prime Minister Narendra Modi. Many others, including German Chancellor Angela Merkel, sent congratulatory telegrams. The White House had said Monday that it was 'not surprised by the outcome' of Sunday's presidential election in Russia and that no congratulatory call was planned. Trump continues to grapple with the shadow of the ongoing investigation into whether his campaign colluded with Russian officials during the 2016 election that sent him to the White House. Last month, special counsel Robert Mueller indicted 13 Russian individuals and three organizations on charges of interfering in the election. Three of Trump's associates — former national security adviser Michael Flynn, deputy campaign chairman Rick Gates and campaign aide George Papadopoulos — have pleaded guilty to lying to investigators and agreed to cooperate. Trump's former campaign chairman Paul Manafort has pleaded not guilty to a variety of money laundering and other criminal charges. ___ Isachenkov reported from Moscow. AP writer Zeke Miller contributed from Washington.