The New Zealand dollar stuck to a tight range as markets await news out of a meeting between US President Donald Trump and North Korean leader Kim Jong Un as well as a raft of central bank meetings this week.

The kiwi traded at US70.36c at 5pm from US70.29c at 8am and US70.31c on Friday in New York.

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The trade-weighted index was at 73.68 from 73.65 last week.

Investors were jittery after Trump pulled out of a Group of Seven communique on the weekend but attention quickly shifted to the Trump-Kim Singapore meeting, set to take place Tuesday. Caution, however, remained.

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The kiwi has "been in a pretty tight band," said Mark Johnson, senior trader foreign exchange at OMF in Wellington.

"The market is lacking a bit of conviction here at the moment."

Regarding the Trump-Kim meeting, he said "any smoothing in relations will be viewed as a step in the right direction", and will be positive for risk. Investors are also preparing for rate decisions and statements from the US Federal Reserve, the European Central Bank and the Bank of Japan this week.

Johnson said markets are waiting to see if the US central bank, which will hold a two-day meeting starting June 12, updates its dot plot to forecast three more rate hikes this year.

However, "why would they necessarily want to be more upbeat than they need to be," he said.

On the ECB, which meets June 14, investors are waiting to see if it signals plans to start unwinding its massive bond-purchasing programme but slightly softer data out of France and Germany of late could mean they are reluctant, he said.

"Growth concerns for the eurozone could lead to a slightly more dovish outlook for the ECB."

It that's the case, a recent rebound in the euro will reverse, he said.

The kiwi traded at 59.63 euro cents from 59.71 cents last week and was little changed at 52.45p from 52.41p.

The kiwi rose to 77.23 yen from 76.96 yen last week.

The kiwi gained to A92.52c from A92.31c on Friday in New York and increased to 4.5070 Chinese yuan from 4.4988 yuan.

New Zealand's two-year swap rate rose 1 basis point to 2.23 per cent and 10-year swaps were unchanged at 3.20 per cent.