NEW YORK (Reuters) - With national security again a major U.S. election issue after bombings in New York and New Jersey, Hillary Clinton and Donald Trump sought to burnish their foreign-policy credentials on Monday by meeting world leaders at the United Nations. For Clinton, the Democratic presidential nominee, it was a return to a role she knows well after she served as President Barack Obama’s secretary of state for four years. Trump, the Republican nominee, is a newcomer to the global stage who is hurriedly trying to play catch-up.  In rapid succession, Clinton met briefly with Japanese Prime Minister Shinzo Abe, Egyptian President Abdel Fattah al-Sisi, and then Ukrainian President Petro Poroshenko. Trump also met Sisi minutes after the Egyptian leader spoke with Clinton in the same Manhattan hotel. The meetings came on a day that started with Clinton suggesting Trump’s harsh rhetoric toward Muslims aids the Islamic State militant group’s recruiting efforts. Trump pushed back, arguing the United States was less safe as a result of Obama and Clinton’s policies. Security questions arose in each of Monday’s bilateral sessions, which took place as world leaders gathered for the U.N. General Assembly, with Clinton and Abe discussing concerns over North Korea and maritime issues involving China.  Clinton and Trump both spoke with Sisi about working more closely with Egypt to combat the Islamic State threat.  Trump’s campaign released a statement saying that Trump “highlighted how Egypt and the U.S. share a common enemy and the importance of working together in defeating radical Islamic terrorism.”  With Clinton, Sisi also discussed his goal of moving Egypt toward “a new civil society, a new modern country that upholds the rule of law and respects human rights and liberties.”  Clinton and Poroshenko addressed Russian incursions into Ukrainian territory. Clinton started the session by saying Ukraine faces “very real problems and threats from Russian aggression” and that she was “anxious to know how we can be supportive.”  The session also resonated because of Trump’s praise of Russian President Vladimir Putin earlier this month. Trump called Putin a stronger leader than Obama, rattling both Democrats and Republicans in Washington.  The evening was not without drama, starting with Clinton’s motorcade zooming through packed New York streets at rush hour and then quickly rushing from hotel to hotel. Trump also tried to bolster his foreign policy credentials last month when he went to Mexico to meet President Enrique Pena Nieto, but both sides ended up disagreeing about whether who would pay to build a border wall had been discussed.  Clinton called that episode an “embarrassing international incident.” 