Can we compress microsecond duration laser pulses by a factor of 1000?

So this is a discharge pumped laser.

At 18 Torr the laser lines will be quite narrow. Do you know how much bandwidth you have in your current output pulses? I think this is important.

You may have the needed bandwidth (~1/1us). If so, then I'll look from a crystal with anomalous dispersion for the compression.

If you do not have the bandwidth then you need to create the bandwidth (see https://en.m.wikipedia.org/wiki/Bandwidth-limited_pulse). I am thinking pressure broadening the spectral lines at 10um is the way to go. If you do not have the bandwidth then compression isn't possible.

( this is the beginning of a full answer. I didn't want the comments to keep expanding)

There are several pulsed lasers available in the market ranging from milisecond to femtosecond (attosecond ??). They all have different purposes and different technology. The CO2 laser you are using will be probably the circulating gas High power CO2 laser. Usually employed in cutting welding drilling etc. First of all you can make the pulse duration shorter just by chopping (you will loose rest of the energy hence only loss no gain). CO2 lasers are available (as far as my knowledge goes) few picosecond short but not at 10.6 micron.

The duration of the laser in your case is limited by the duration of the discharge and not by the bandwidth of the laser. If you can decrease the duration of the discharge you can compress the laser pulse duration (I dont know if it is at all possible).

The duration of your laser is too long to be compressed externally. The basic principle of the external pulse compression is to device a way such that the earlier portion travel larger optical path than the latter portion and then synchronize them to make a short pulse. This method can be used to compressed picosecond pulses to femtoseconds, microsecond pulses to submicrosecond or nanoseconds but I could not think any external method to generate the short pulse in your case by 'external' means.

you may employ the technique known as 'Q' switching to decrease the pulse duration. In q switching you increase the loss in the laser cavity during the pumping and then suddenly decrease the loss (when the population inversion is at its peak) in such case the population inversion is depleted in few round trips and you get the short pulse.

Here you may note that in order to successfully employ the Q switching the duration of the pumping must be smaller than the lifetime of laser cycle or the population inversion will be deexcited via spontaneous emission route.

EDIT: The time bandwidth product hold true only for mode locked laser pulses. Usually in other pulsed lasers the bandwidth is much higher than required minimum. For ex for CO2 laser the required bandwidth for ms pulses is $\Delta\lambda \sim3.7\times10^{-10}$ micron for microsecond pulses it become $\Delta\lambda \sim3.7\times10^{-7}$ micron (no limitation posed by bandwidth) for picosecond pulses this will become $0.37$ micron (you should now be concerned). Note that above numbers are just for indication as the actual time bandwidth product depends on pulse shape.

Note:

1. It is certainly possible that one can generate 1 ps CO2 laser pulses infect the theoretical limit is ~35 fs (single cycle pulse) but it is not possible to compress a millisecond pulse and make it microsecond. One may argue that if we can compress 1 nanosecond (stretched) pulse to 30-50 femtosecond femtosecond duration (factor of $10^{4-5}$) then why the same ratio can not be achieved for millisecond pulses, in this situation one must know that the length of the stretcher/compressor increased linearly with the length of the maximum pulse duration.
2. It may be noted that any conventional stretcher/compressor that can be used to compress millisecond pulses must have dimensions ~100-1000 km.

Solution

There is only one solution to this problem, change the design of the laser such that the discharge timings decreases to microsecond levels. People have used RF discharge to generate microsecond CO2 lasers.