Some of this has coincided with the launch mid-May of Operation Mountain Thrust, the biggest anti-Taliban operation yet which involves around 10,000 soldiers and support staff including from the Afghan, British, Canadian and US forces.
The coalition says the increase in fighting is in part because the boosted force can penetrate remote areas that were previously free of government authority for years.
In the other coalition fatalities in the past week, a soldier died in a bomb blast in Kandahar province on June 20 and four US soldiers were killed in eastern Nuristan the following day.
Three other soldiers died from wounds sustained in battle, the coalition has said.
Despite the presence of thousands of troops in Afghanistan, the violence has shown no signs of abating and is further demoralising a population already frustrated with the lack of major improvement to their lives since the Taliban were ousted nearly five years ago.
Afghan officials have said violence is continuing in part because the leaders of the rebellion and suppliers of soldiers and weapons are based in neighbouring Pakistan, which nurtured the Taliban into an militia force in the early 1990s. Pakistan denies the charge.
US Secretary of State Condoleezza Rice said she would press during talks in Islamabad on Tuesday for greater anti-terrorism cooperation between Pakistan and Afghanistan.
Shortly before arrival in Islamabad she said she would visit Afghanistan also.