The Maryland Senate yesterday easily approved a bill increasing the maximum weekly unemployment benefit from $153 to $165. The increase was part of an overall unemployment compensation package worked out by legislative leaders and Gov. Harry Hughes.

The bill also will extend the additional benefits program that provides 13 extra weeks of state unemployment pay after regular benefits have run out, and will increase taxes levied on employers.

The increases are necessary to raise money for the state's hard-pressed unemployment compensation trust fund, through which jobless benefits are paid. Without the tax increase the fund could run out of money by December, forcing Maryland to borrow from the federal government.

The unemployment package, which passed by a vote of 44 to 2, now goes to the House for concurrence. The House had passed the unemployment bill about two weeks ago, but with a smaller, $7 increase in the weekly benefit. That version of the measure also used a different formula to calculate the new tax on employers.

These differences will have to be resolved in a conference committee, House leaders said yesterday. They said it was possible that the $12 increase approved by the Senate would be reduced in the House.