Mr Pence said the USA would "abandon the failed policy of strategic patience" with North Korea but would redouble efforts to bring diplomatic and economic pressure to peacefully decrease tensions.
The Trump administration has said military action remains an option for dealing with North Korea.
Pence warned North Korea to not test the resolve of the United States "or the strength of our military forces".
North Korea regularly threatens to destroy Japan, South Korea and the United States and it showed no let-up in its defiance after a failed missile test on Sunday, a day after putting on a huge display of missiles in Pyongyang.
Talking to ABC radio, Ms Bishop said the North Korean threat to regional and global peace has increased and any rise in tensions is entirely due to its provocative behaviour. Any missile or nuclear strike by the United States would be responded to "in kind", said the North Korea representative. In fact during six party talks in 2005, North Korea had reached an agreement to suspend its nuclear programme in return for diplomatic rewards and energy assistance.
"The era of strategic patience is over and while all options are on the table, President (Donald) Trump is determined to work closely with Japan, with South Korea, with all our allies in the region and with China to achieve a peaceable resolution and the denuclearization of the Korean peninsula" Pence said in Tokyo before lunch with Prime Minister Shinzo Abe.
"North Korea is to be prevented from carrying out further tests but this can be done in many ways", Ms Bishop said.
"The Trump administration has explicitly rejected President Obama's approach of strategic patience because that led to a stalemate, during which time North Korea's illegal missile and nuclear program accelerated", she told AM.
Burying 'Trumpomania,' Kremlin TV says Trump scarier than North Korean leader
An improved relationship could also lead to the easing of sanctions imposed by the west over Russia's incursion into Ukraine. Officials privately say they regard many of Mr Trump's policy positions as no different to, or tougher than, Mr Obama's.
The US and South Korea have activated the Terminal High Altitude Area Defence (THAAD) system, which is capable of intercepting incoming warheads from North Korea.
In Japan, they said Pence's two main goals are to spur increased US access to Japanese markets and strengthen Japanese foreign investment.
He referred to the U.S. bombing of a Syrian air base on April 7 to punish the Bashar al-Assad regime for a suspected use of chemical weapons.
South Korea's acting president, Hwang Kyo-ahn, told a cabinet meeting on Tuesday that South Korea would strengthen its alliance with the United States and closely cooperate with China to rein in North Korea.
The Foreign Minister reiterated calls for China to use its unique and potentially decisive leverage against the North Korean regime.
China is one of North Korea's few allies and accounts for three-quarters of its exports and nearly all direct investment and in the country.
Both sides said they do not expect the talks in Tokyo this week to delve into sector-by-sector talks on trade.
"We support the U.S. putting pressure on Chinese banks to ensure that the elites in North Korea can not continue to live the comfortable lives that they now do while the people of North Korea are suffering".
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