U.S. builders began work on more office buildings, shopping centers, and hotels in June, pushing construction spending higher for a third consecutive month, the Commerce Department said Monday. Construction spending rose 0.2 percent in June to an annual rate of $772.3 billion, the department reported. That put overall spending just 1.2 percent higher than the 11-year low hit in March, and it is just half of the $1.5 trillion pace considered healthy by most economists. In June, residential construction declined, reflecting a big drop in apartment construction, and spending on government building projects also fell. But private nonresidential activity rose to the highest level since late 2010. In June, private residential construction dropped 0.3 percent to a seasonally adjusted $235.8 billion with a 0.3 percent rise in single-family home building offset by a 2.8 percent drop in the apartment sector. The 1.8 percent rise nonresidential construction pushed this sector to $257.7 billion, the highest level since December 2010 with a number of commercial projects including hotels, office building, and shopping centers all showing gains. Government building projects fell 0.7 percent to an annual rate of $278.9 billion, the lowest level since March 2007. Budget cuts at the state and local levels have led to a sharp drop in government spending.