Most emerging market (EM) stocks and currencies tiptoed higher on Monday as the dollar felt pressure globally heading into Donald Trump's inauguration as U.S. president later in the day.

Investors were largely in watch mode given the uncertainty Trump poses for developing economies. The main global gauge of EM currencies was up 0.2% on the day but is down more than 2% since Trump won election in November.

Overnight in Asia, the battered Chinese yuan, the Indian rupee and Korean won all nudged higher. South Africa's rand then did the same along with most of emerging Europe, including a 0.3% gain for the Hungarian forint.

Monday's early fireworks though came in Mozambique where its sole international market bond tumbled almost 2.5 cents on the dollar after Bloomberg reported that the new government is weighing a debt restructuring.

That follows weeks of deadly protests in the wake of a hotly contested presidential election in October.

Mexico, which has some of the most widely traded currency and bond markets in emerging markets, is likely to be in the spotlight with Trump expected to kick off by cracking down on illegal immigration within hours of his swearing-in.

The Mexican peso has depreciated more than 3.5% since November but is down much more over the last year as its domestic politics have also caused unease for investors.

The threat of tariffs has overshadowed the outlook for growth across EMs, with local markets also grappling with the possibility of Fed interest rates remaining elevated for longer if tariffs and tax cuts keep U.S. inflation up.

Despite Monday's weakness, the dollar index - which measures the greenback against a basket of major peers - is hovering near its highest level in over two years.

"FX markets are overvaluing the broad dollar (DXY) by around 3%, similar to over-valuation levels observed during Trump's first term (in 2017-21)," said Robert Sockin, senior global economist at Citi.

"This type of trade action suggests markets are not expecting tariff policies to reach some of the extremes outlined during Trump's campaign. But if such policies eventually materialise, it could push the US dollar even higher."

MSCI's index for emerging market stocks added 0.8%, boosted by strong gains in Hong Kong and India - some of the biggest weights on the index.

Chinese equities, meanwhile, closed higher. Last week, Trump said he discussed trade, fentanyl and Tik Tok with Chinese President Xi Jinping, saying their phone call "was a very good one for both China and the US."

Over the weekend Trump also moved to prevent a US ban on TikTok coming into force, saying: "Frankly, we have no choice. We have to save it."

In the Middle East, Hamas released three Israeli hostages in Gaza and Israel freed 90 Palestinian prisoners on Sunday, the first day of a ceasefire suspending their 15-month-old war.

The Israeli shekel was last down 0.5% following its near 1.5% jump on Friday. Hard currency debt of both Israel and Lebanon was largely flat on the day.