SAN FRANCISCO — Elliott Management, the $27 billion hedge fund with a penchant for shaking up technology companies, has found itself two new targets in the industry — and is urging them to combine.

The activist hedge fund disclosed on Thursday that it had acquired a 6.6 percent stake in Polycom and a 6.3 percent stake in Mitel, making the firm among the biggest shareholders in both companies.

Elliott recommended that the two providers of voice and video communications equipment merge, as part of a potential wave of consolidation in the telecom equipment sector.

Shares in Polycom were up 13 percent in midmorning trading on Thursday, giving it a market value of nearly $1.6 billion. Shares in Mitel were up 16 percent, valuing the company at about $1.1 billion.