The white House said Chinese President Xi Jinping and US President Donald Trump had spoken by telephone about keeping pressure on North Korea using economic sanctions imposed through the United Nations.
Her visit raised suspicion whether the United States was actually considering a pre-emptive attack on North Korea, but an official from the USA military denied the speculation, saying Cordray had previously visited in May and that her most recent trip was part of a routine check of local systems.
Spain on Monday ordered North Korea's ambassador to leave the country by September 30 in protest over Pyongyang's nuclear tests, which it has criticized as "a serious threat to peace".
Separately, China and Russian Federation began a joint naval exercise east of the Korean peninsula.
The US jets flew alongside four South Korean F-15K jet fighters as part of "routine" training, the statement said, adding that the allies would continue such exercises to "improve their joint operation capabilities against contingencies".
The ruling Democratic Party is urging for a peaceful resolution to the North Korean issue.
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North Korea has said it is developing a long-range missile force capable of delivering a nuclear weapon to US territory.
Asked whether there were any military options the United States could take with North Korea that would not put Seoul at grave risk, Mattis said: "Yes there are". Japan deployed today an additional missile defence system on its northern island of Hokkaido, days after North Korea launched a missile over the island, sparking emergency warnings to take cover.
Instead, he said, the global community should strictly implement the sanctions imposed on North Korea by the U.N. Security Council.
North Korea - the Democratic People's Republic of Korea (DPRK) - has repeatedly conducted missile launches in recent months, despite being barred from doing so under United Nations rules.
German Foreign Minister Sigmar Gabriel also said in comments reported Monday by the Bild daily that the world should wait for the sanctions to bite, but that "visions and courageous steps" such as direct negotiations with North Korea are also needed.