Pressure is building on U.S. President Donald Trump to take tougher actions against Russia, an expert said on Wednesday after the U.S. Treasury announced a series of new sanctions on Moscow.

Calls for more potent measures to punish Russia are coming from both within and outside the U.S.

Russia, under President Vladimir Putin, has been accused of undermining democracies and violating international rules with activities including tampering with the U.S. election and poisoning a former Russian spy in the U.K.

"There're a lot of things going on right now that are calling for (an) increase in sanctions against Russia," Eugene Chausovsky, senior Eurasia analyst at consulting firm Stratfor, told CNBC's "The Rundown" on Wednesday.

Domestically, criminal charges against two of Trump's former aides — campaign manager Paul Manafort and long-time lawyer Michael Cohen — could strengthen the case for Justice Department special counsel Robert Mueller's probe to continue, Chausovsky said. Mueller is investigating possible Russian interference in the 2016 U.S. presidential election. Manafort's trial was a major victory for Mueller's probe, and Cohen came under investigation by federal prosecutors in New York City after a referral by the special counsel's team.

Several members in Congress have also questioned whether the Trump administration has gone far enough to rein in the Kremlin's behavior, The Wall Street Journal reported.

Internationally, U.K. Foreign Secretary Jeremy Hunt on Tuesday urged the European Union to "stand shoulder to shoulder" with the U.S. in sanctioning Russia.

The U.S. Treasury on Tuesday said it blacklisted two Russian companies and six vessels for violating United Nations sanctions on North Korea. In addition, two other firms — one Russian and one Slovakian — along with two Russian individuals were called out for helping another company avoid U.S. sanctions.

Those latest actions by the U.S. are "mild," said Chausovsky, because they target specific companies and individuals for "very specific issues." But tougher sanctions against an entire industry in Russia or very large Russian companies could come in the next few months, he added.