By Jeff Mason

HAMBURG (Reuters) - U.S. Secretary of State Rex Tillerson said on Friday there would not be many good options left on North Korea if the peaceful pressure campaign the United States has been pushing to curb Pyongyang's nuclear and missile programs failed.

"We have not given up hope," Tillerson told reporters after U.S. President Donald Trump and Russian President Vladimir Putin met on the sidelines of a G20 summit, just days after North Korea conducted what it said was its first test of an intercontinental ballistic missile (ICBM).

Tillerson said the U.S. approach of stepping up pressure on North Korea through sanctions required patience.

"I call it the peaceful pressure campaign ... This is a campaign to lead us to a peaceful resolution because if this fails, we don't have very many good options left," he said. "It's one that requires calculated increases in pressure, allow the regime to respond to that pressure, and it takes a little time to let these things happen."

The United States, Japan and South Korea agreed on Friday to push for a quick U.N. Security Council resolution to apply new sanctions on North Korea. U.N. diplomats said the United States had given China a draft sanctions resolution.

But Washington faces an uphill struggle to convince Russia and China to give quick backing to new U.N. sanctions.

Experts say North Korea's ICBM launch on Tuesday was a major step forward in its declared intent to create nuclear-tipped missiles capable of hitting the United States. Some U.S. experts say the missile appeared to have the range to hit Alaska, Hawaii and parts of the U.S. Pacific Northwest.

Washington has warned it is ready to use force if need be to stop North Korea's weapons programs but the consequences of that could be catastrophic and it prefers global diplomatic action.

Russia has said further sanctions will not resolve the issue and on Thursday objected to a U.N. Security Council condemnation of North Korea's launch because the U.S.-drafted statement labelled it an ICBM, a designation Moscow disagrees with. Diplomats said on Friday that negotiations on the statement had stalled.

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Tillerson said Trump and Putin held differing views on how to deal with North Korea but that Washington would continue to press Moscow to help.

"We're going to continue those discussions and ask them to do more. Russia does have economic activity with North Korea," he said.

TRUMP TO MEET CHINESE LEADER

Trump is due to meet Chinese President Xi Jinping, whose country is North Korea's main trading partner, on the sidelines of the G20 on Saturday. Trump has warned Beijing it could face U.S. economic and trade pressure unless it does more to rein in North Korea.

Tillerson said China's responses to U.S. calls for it step up pressure on North Korea had been uneven.

"China has taken significant action and then I think for a lot of different reasons, they’ve paused and didn’t take additional action," he said.

Referring to a U.S. decision last week to impose unilateral sanctions on two Chinese individuals and a shipping firm and to accuse a Chinese bank of money laundering, he said:

"We've continued to make that clear to China that we would prefer they take the action themselves and we're still calling upon them to do that."

Tillerson said a Chinese and Russian proposal for the United States and South Korea to suspend joint military exercises in return for a freeze in North Korean weapons testing was unacceptable as it would freeze North Korea's programs at too high a level of capability.

"We're asking North Korea to be prepared to come to the table with an understanding that these talks are going to be about how do we help you chart a course to cease and roll back your nuclear program. That's what we want to talk about.

"We're not interested in talking about how do we have you stop where you are today."

North Korea on Friday described Tuesday's missile test as a "gift package" and vowed to deliver more.

“The U.S. will receive more ‘gift packages’ of different sizes from the DPRK (North Korea) in endless succession, as it tries harder to destroy, by means of sanctions and pressure, the overall national power and strategic position of the DPRK which have been drastically boosted,” the official KCNA news agency quoted a Foreign Ministry spokesman as saying.

The U.S. ambassador to the United Nations, Nikki Haley, said on Wednesday she would propose new sanctions to the 15-member U.N. Security Council in coming days.

Traditionally, the United States and China have negotiated new sanctions on North Korea before formally involving other council members.

Following a nuclear weapons test by North Korea in September it took the U.N. Security Council three months to agree strengthened sanctions.

(Reporting by Tim Ahmann, David Alexander and David Brunnstrom in Washington and Michelle Nichols at the United Nations; Writing by David Brunnstrom; Editing by James Dalgleish and Bill Trott)