Global equities posted muted gains Tuesday, as investors digested U.S. President Donald Trump's announcement of a ceasefire timeline between Iran and Israel, as well as growing signs of fatigue toward Trump's policymaking.

The MSCI World index, which tracks over a thousand large and mid-cap companies from 23 developed markets, was just 0.24% higher as of 1 p.m. Singapore time.

U.S. futures were also up marginally. Futures tied to the Dow Jones Industrial Average inched higher by 0.71%. S&P 500 futures gained 0.74%, while the Nasdaq 100 futures rose 0.98%.

While Asian equities edged higher, broader gauges of investor sentiment remained relatively subdued, reflecting a market that is potentially getting desensitized by America's policymaking.

"The markets are muted again for two reasons. Number one is there are elements of the market getting jaded at Trump policy changes, though this has been going on for a while," said Hugh Dive, chief investment officer at Atlas Funds Management.

Dive added that the second reason would be how the Iranian response to U.S. strikes on its nuclear facilities was largely subdued. On Monday, a missile strike by Iran on a U.S. airbase in Qatar left no reported casualties. 

After the wild swings from changes to tariff policy in April, each successive change has seen less of a move, Dive pointed out. 

"Winding back the alarming headline moves in tariffs has seen subsequent shocks less," he told CNBC.

Since the start of the year, Trump's pattern of threatening steep tariffs and policies that rattle markets, only to ease or postpone them after a sharp market sell-off, prompted a phrase that has ruffled the president's feathers — "Trump Always Chickens Out."

Some also saw Middle East de-escalation on the cards.

While Iran's Foreign Minister Seyed Abbas Araghchi refuted claims that Tehran had agreed to a U.S.-brokered ceasefire deal with Israel, he signaled that his country was ready to stop hostilities.

"In reality, I think markets focus very quickly on the likelihood that the geopolitics allowed Iran to think about what their response would be. And I think that de-escalation seemed a likely event," said Vis Nayar, chief investment officer at Eastspring Investments.

The reported ceasefire is "the most bullish outcome" Wall Street could hope for, said Dan Ives, managing director at Wedbush Securities, who believes that U.S. markets should rally once they start trading on Tuesday.

"Some will say the ceasefire will not last but the reality is Iran has limited options and negotiations will now take over which is a positive for stocks," Ives added.

Safe haven assets, which typically sees more selloff in perceived times of peace, saw a marginal selling down.

Yields on the 10-year Japanese government bond, another typical safe haven, was up only a little by around 1 basis point to 1.425%.

The Swiss franc stayed firm at 0.8114 against the  greenback. The U.S. dollar index, which measures the greenback's strength against a basket of currencies, slid 0.29%.