Japan's declined 0.44 percent, or 99.81 points, to close at 22,408.88 as most sectors traded in negative territory, although gains were seen in the mining and banking sectors.
Elsewhere, South Korea's benchmark Kospi edged down by 0.24 percent to 2,443.98. Despite the benchmark's overall decline, gains were still seen in petroleum refiners, with SK Innovation up 1 percent. The junior Kosdaq jumped 2.86 percent.
Greater China markets searched for direction. Hong Kong's tacked on 0.2 percent by 3:17 p.m. HK/SIN after hovering around the flat line earlier in the day. Gains were led by the energy sector, which was up 1.83 percent before the market close as CNOOC rose 1.82 percent. Technology stocks also recorded moderate gains in afternoon trade.
Mainland markets finished the day slightly lower. The slipped 0.08 percent to close at 3,158.81 and the Shenzhen composite eased by 0.09 percent.
Down Under, the S&P/ASX 200 tacked on 0.26 percent to end at 6,108 as a decline in the heavily weighted financials subindex were offset by gains seen in most other sectors. The energy subindex rose 1.34 percent as oil producers advanced, with Woodside Petroleum up 1.22 percent for the day.
MSCI's broad index of shares in Asia Pacific excluding Japan slipped 0.21 percent in Asia afternoon trade.
Trump on Tuesday delivered on a pledge made during his election campaign to withdraw the U.S. from the 2015 Iran agreement, announcing that broad sanctions would be reimposed on the country.
The landmark accord lifted international sanctions on Iran in exchange for the country curbing its nuclear program. Iran says it will stay committed to the agreement and will continue negotiating with other parties to the deal, Reuters reported.
"It is still not known [what] the wider implications of the U.S. pulling out mean for the deal," said ANZ analysts, adding that Trump's announcement "puts into place a scenario that could see the crude oil market tighten significantly" in the second half of this year and into 2019.
Oil gained on Wednesday, touching their highest levels since November 2014: U.S. West Texas Intermediate rose 2.85 percent to trade at $71.03 per barrel. U.S. crude futures had crossed the $70 level for the first time since end-2014 on Monday.
Brent crude futures were up 2.93 percent at $77.04.
Although renewed U.S. sanctions on Iran will reduce Iranian crude exports, "compliance with unilateral U.S. sanctions would be much more difficult to enforce than the multilateral measures implemented in 2012," Paul Sheldon, associate director at Platts Analytics, said in a note.
Oil prices had declined in the last session although they settled above their session lows following Trump's announcement.
The slight declines seen in Asia also came on the back of U.S. stocks finishing little changed on the back of Trump's announcement, with the Dow Jones industrial average closing up 0.01 percent and the S&P 500 ending lower by 0.03 percent.
In currencies, the dollar extended its gains against a basket of currencies. The dollar index traded at 93.386 at 3:13 p.m. HK/SIN.
Against the yen, the dollar strengthened some 0.5 percent to trade at 109.71 — its strongest level in more than a week. The Australian dollar, meanwhile, slipped to trade at $0.7417 amid broader strength in the dollar.
In individual movers, Toyota announced it was expecting a 4.2 percent decline in operating profit this financial year. Shares of the automaker rose 3.76 percent, outperforming other major Japanese automakers, which declined.