Obama called Hu to ask him to tell North Korea that its recent actions are unacceptable.
In November, North Korea shelled a front-line South Korean island, resulting in four deaths - two South Korean marines and two civilians. Also, the North is pursuing a uranium enrichment program.
Monday, the prosecutor of the International Criminal Court opened a preliminary investigation into possible war crimes by North Korea resulting from its Nov. 23 shelling of Yeonpyeong Island. The investigation will also look into the sinking of South Korean warship, the Cheonan in March.
The new round of artillery exercises launched by the South is set to continue through Sunday, army and Joint Chiefs of Staff officials said.
The Associated Press contributed to this report.