The new proposals could increase US tax revenue by $210bn over the next decade if it is approved by the US congress, but they are likely to be strongly resisted by US corporations.
Under the plan, the Internal Revenue Service (IRS) will get nearly 800 new agents to pursue offshore tax avoidance.
He also called for more transparency in bank accounts held by US citizens in tax havens such as the Cayman Islands.
"If financial institutions won't co-operate with us, we will assume that they are sheltering money in tax havens and act accordingly,'' Obama said.
The current rules allow US firms to defer paying taxes on profits earned overseas if they invest those profits back into their foreign subsidiaries.
A number of major US firms have already registered their opposition to changes to the "deferral" provision.
Pfizer, Oracle, Microsoft, Johnson & Johnson and General Electric were among 200 firms who signed a letter to US congressional leaders opposing the move.