We demonstrate a method to synthesize ultra-high repetition rate bursts of ultrashort laser pulses containing any number of pulses within a burst with identical pulse separation and adjustable amplitude. The key element to synthesize the GHz bursts of ultrashort laser pulses is an active fiber loop. The method was implemented in the fiber chirped pulse amplification system to obtain 72 nJ-energy bursts of 20 pulses with a 2.65 GHz intra-burst pulse repetition rate and a 500 kHz burst repetition rate. The dispersion compensation mechanism ensured a mean pulse duration of 570 fs within the bursts.