- Attack occurred on Christmas Day in Iraq and Afghanistan
- In Iraq, the attacks targeted Christians
- In Afghanistan, the attack at the U.S. Embassy compound
(CNN) -- Two car bombs targeting Christians killed at least 35 people in southern Baghdad on Christmas.
In Afghanistan, two rounds of "indirect fire" hit the U.S. Embassy compound in Kabul -- but no one was hurt.
The incidents highlight the security challenges that both Iraq and Afghanistan are grappling with.
Both countries have had a heavy U.S. military presence until recently.
The departure of U.S. forces from Iraq has done little to curb the near-daily cycle of violence. In Afghanistan, U.S. and Afghan officials are working on an important security pact to outline the future of American troops in Afghanistan.
Iraq attacks
In Iraq, a car bomb exploded outside a church in southern Baghdad just as worshipers were leaving a Christmas Day service, killing many. In another nearby attack in the al-Dora district Wednesday, another car bomb went off at an outdoor market where many Christians shop, police said.
Altogether, at least 35 people were killed and some 56 others were wounded, the Interior Ministry said.
Afghanistan attack
Two rounds of "indirect fire" hit the U.S. Embassy compound in Kabul, the embassy said. No one was injured.
"At approximately 6:40 local time in Kabul, approximately two rounds of indirect fire impacted the U.S. Embassy compound. All Americans are accounted for and no injuries were sustained," the embassy said in a statement Wednesday. "The Embassy continues to investigate the attack."
The embassy did not elaborate on what kind of rounds were fired, or where in the compound they landed.
No group immediately claimed responsibility for the attack. CNN was waiting to hear back from the State Department.
The incident comes at a pivotal time in U.S. and Afghanistan relations. The two countries are working on an important security pact. The deal will lay out out the U.S. military presence in Afghanistan after 2014, when the NATO-led force of some 80,000 troops is scheduled to leave.
Earlier this month, U.S. Defense Secretary Chuck Hagel was in Afghanistan and said the security pact will be agreed upon despite a failure so far to forge a deal.
CNN's Mohammed Tawfeeq contributed to this report.
