A policeman stands guard next to the scene where a blast ripped through a church in Nairobi on September 30, 2012.

Story highlights

NEW: Kenyan military moves into key port city, takes control of police station

One child dead, the Kenya Red Cross says

A Kenyan hospital reports 7 injured, two of them critically

Attacks have escalated since Kenyan forces invaded Somalia to battle Islamist militants

Nairobi, Kenya CNN  — 

One child died and several others were hurt in a grenade attack on a children’s Sunday-school class in Kenya, the Kenya Red Cross said.

A Kenyan hospital reported seven children wounded.

The Kenya Red Cross and local media described the incident at St. Polycarp church in Nairobi as a grenade attack. Government officials did not answer repeated telephone calls from CNN seeking comment.

Four injured children were admitted to Kenyatta National Hospital – two for treatment of critical wounds, said Dr. Mutie Thomas, the hospital’s senior assistant director.

Doctors treated and released another three people, Thomas said.

The injuries involve soft tissue damage, head wounds and broken bones, Thomas said.

The children were between the ages of 7 and 10.

The Kenya Red Cross tweeted that one child died, and that “six critical children” were taken to a hospital.

Such attacks have escalated since Kenyan forces invaded neighboring Somalia last year to battle the Islamist militant group al-Shabaab, blaming it for kidnappings of foreigners in the nation.

The main force of Kenyan and Somali troops have taken control of police headquarters, a radio station and a seaport of the port city of Kismayo, Somalia, the Kenya Defence Forces announced on Twitter Sunday.

As the joint forces gain ground, “this has given an added impetus to the Somali peace process,” the Kenyan military said.

An advance unit landed on the beaches north of the city on Friday and has secured northern parts of the town, the university and one important highway, according to the military’s Twitter account.

A Kenyan military spokesman said Saturday that the operation was going well.

“Al-Shabaab has not been able to offer any resistance whatsoever to the ground forces since the ground forces landed there yesterday, and the whole of yesterday and the good part of today they have (suffered) heavy casualties,” he said.

In a series of posts Saturday on a Twitter account often used by Al-Shabaab, the group said the Kenyan military is “waging a losing battle” in Kismayo. It said mujahedeen forces ambushed Kenyan troops 30 km (18 miles) west of Kismayo, destroying three vehicles and killing dozens of troops in a two-hour battle.

The military spokesman said those reports are “pure propaganda.”

On Sunday Al-Shabaab said on the Twitter account: “The shelling of the city lays bare the intentions of KDF invaders & reveals that their war isn’t just against (Al-Shabaab) but the Muslims of Somalia.”

Al-Shabaab uses Kismayo to make money from the illegal charcoal trade and smuggling. Thousands of residents of the city fled before the fighting, according to the U.N.