At the UN General Assembly in New York, she said the UK would not "walk away from our partners in the world".
She announced that hundreds of British troops will be sent to Somalia to help combat al-Shabaab jihadists.
And she urged leaders to work together to tackle "the big security and human rights challenges of our time".
Mrs May warned that people felt left behind by the "increasing pace of globalisation".
Mrs May - who also addressed the UN summit on refugees on Monday - said the organisation was "uniquely placed" to tackle war, terrorism, climate change, human trafficking and mass migration.
"The biggest threats to our prosperity and security do not recognise or respect international borders," she said, adding: "And that if we only focus on what we do at home, the job is barely half done."
Mrs May will also hold a series of face-to-face meetings with other leaders and take part in a summit on refugees called by US president Barack Obama.
In his final address to the general assembly, President Obama said countries should do more to help refugees, "even when the politics are hard".
"We have to imagine what it would be like for our family, for our children, if the unspeakable happened to us," he said.
"And we should all understand that ultimately our world will be more secure if we are prepared to help those in need and the nations who are carrying the largest burden with respect to accommodating these refugees."
BBCNEWS
BBCNEWS