Meanwhile, Pence reassured Japanese Prime Minister Shonzo Abe that the United States' support for Japan is 100% amid the increasing provocations from North Korea.
The North has warned of a nuclear strike against the United States if provoked.
He leveled sharp criticism at the USA and South Korea for conducting the war games of unprecedented scope and scale and said they could entail dire consequences for peace in the region.
He added that Washington expected Japan to play a larger role in the bilateral strategic alliance in the coming years.
Responding to a question on recent comments made by U.S. Vice President Mike Pence, the Russian foreign minister said he hoped the U.S. would not employ tactics similar to the recent Syria strike on the Korean Peninsula.
President Trump received a dire warning from his predecessor, President Obama, about a major national security threat he'd face upon entering the Oval Office: the impulsive dictator of a nuclear-armed North Korea, Kim Jong-un, who is suspected of assassinating his own half-brother, executing his uncle and disposing of high-ranking military officials at will.
Han reiterated North Korea's position that it would react with a "nuclear pre-emptive strike by our own style and method" should the USA plan a military attack on the country.
President Trump has signaled that he will not hesitate to take military action against enemies of the United States, as evidenced by his bombing of a Syrian airfield and an ISIS cave in Afghanistan last week.
USA top diplomat warns of Iran 'provocations'
Obama argued the deal was narrowly tailored to prevent what he said was the imminent emergence of a nuclear-armed Iran . And he said the United States wanted to change course before Iran became a "second piece of evidence" for this.
Trump, asked on Monday if he was considering military action, told Fox News Channel he did not want to "telegraph" his plans, like the previous administration had done. According to USA officials, the missile exploded four to five seconds after being launched from a location near a North Korean submarine base in Sinpo along the country's eastern coast.
At the outset of their meeting, Pence reiterated to Abe his statement in South Korea that the United States has run out of patience with Pyongyang's moves. His national security adviser, H.R. McMaster, said the US would rely on its allies as well as Chinese leadership to resolve the issues with North Korea.
"I have absolute confidence that he will be trying very hard" to handle North Korea, Trump said of Xi.
The isolated country's military will mark the 85th anniversary of the founding of the Korean People's Army on Tuesday amid speculation Pyongyang will use the occasion to test-launch a ballistic missile or conduct a nuclear test.
While North Korea's missile test failed on Sunday, the regime's vice foreign minister, Han Song-Ryol, told BBC that NoKor will be "conducting more missile tests on a weekly, monthly, and yearly basis".
Pence also said the US would protect freedom of navigation in the South China Sea, the sea lanes vital to global shipping where China has been staking claim to disputed territory. They agree it's their first choice.
The Russian diplomat also took a hard line on the previous USA administration's North Korea policies. With no USA trade representative yet in office and other key positions still unfilled, such nitty-gritty discussions will have to come later.