Anti-American protests have been building
Police scuffled with protesters outside a military airport on the outskirts of Seoul, and there were protests in other cities.
During his stay, Mr Bush will get the chance to see North Korea for himself, when he travels on Wednesday to look across the heavily fortified demilitarised zone (DMZ) that divides the Korean peninsula.
The US president arrived from Japan, where he warned that weapons of mass destruction and the proliferation of missile technology threaten the stability of Asia and the world.
Despite the anti-American protests, other demonstrators had planned a warmer welcome for the US president.
Near the Seoul headquarters of the 37,000 US troops in South Korea, several hundred people carried pro-US slogans.
"If you leave Korea today, the communists will be here tomorrow," said one banner.
Cloud over sunshine policy
But outside the military air base where Mr Bush landed, riot police tangled with a crowd carrying their own slogans reading: "No Bush, No War."
The BBC's Caroline Gluck in Seoul says Mr Bush's tough comments about North Korea have disappointed many South Koreans who backed their president's trademark but now faltering "sunshine policy" of engagement.
However, she says some are receptive to the US line, believing too many concessions have been made to the North with to little gained in return.
In an effort to publicly paper over their differences, President Bush is expected to repeat his support for President Kim Dae-jun'gs reconciliation efforts with the North.
And a foreign ministry spokesman told the BBC that Seoul and Washington share the same concerns with regard to Pyongyang's weapons of mass destruction, and would jointly call on North Korea to return to the negotiating table.
As well as going to see the DMZ, Mr Bush will make a symbolic visit to a newly opened station on a rebuilt railway line which would connect the two Koreas.
Protection pledge
While Mr Bush has softened his rhetoric during his tour, his speech to the Japanese parliament warned of the threat to Asia's stability from weapons of mass destruction - a clear reference to North Korea.
He promised to use "American power" to support Washington's allies in the region and deter aggression.
"And to help protect the people of this region, and our friend and allies in every region, we will press on with an effective programme of missile defences," he said.
Mr Bush leaves for China, the final leg of his tour, on Thursday.