This would also be something of my interest. At the moment, I have been using the "High Voltage Power MOSFET" IXTT02N450HV. It works up to 4.5 kV but only 2 kV for DC. I believe its datasheet does not mention about the leakage current.

I have seen a conference paper called "10 kV SiC BJTs – static, switching and reliability characteristics". However, the current leakage is about 1 µA for Vce = 5 kV and temperature of 125°C.  Maybe this figure decreases for other conditions.

Thanks for the reply. I checked the datasheet : apparently the leakage for the transistor you use (Idss for Vgs=0V) is 5µA for Vds=3.6 kV (too high).

Many transistors/diodes I've seen, designed for high voltage applications are also designed for high currents and therefore most of the time the reverse current is about 1µA (which is too high for my application). 

If worse comes to worst you could try to cool the devices down having in mind that the reverse saturation current depends strongly on temperature (rule of thumb: for every 10 deg temp rise the reverse saturation current doubles)

Another possibility is to consider vacuum devices.

That is an interesting solution for the problem. The following link shows the variation of leakage current with temperature:

http://www.genesicsemi.com/images/references/trade_journals/pet_11-11.pdf

With commercial Peltier elements, you can cool the transistor easily down to temperatures bellow 0°C and if you use vacuum, there would not be any condensation of water on it. Using something like this, it might be possible to reach leakage currents close to the desired range. 

Just to add something - care should be taken if one wants to connect more than one device in series because the one with lowest Ir will get nearly the whole voltage... and break down. 

But a nit solution could be if the devices are individually cooled and the cooling is controlled according to the voltage across each device. The system would be slow to turn-on but would probably not need equalizing resistive divider.

May be passive temp self regulation is possible as well - if the breakdown current is limited (and the energy stored in the parasitic capacitance is not enough to damage the junction) and the voltage is ramped  up slowly enough - the one that just starts to breakdown will dissipate a bit more power, leading to junction temperature increase and respectively Ir increase, self regulating the voltage over it. 

Shankar Ekkanath Madathil you said that such component doesn't exist. This is possibly because there are very few applications of high voltage combined with small currents. For diodes there are some having very small leakage current but the reverse voltage is quite small (50 v). I tried to connect 20 diodes in series and it seemed to work at 1kV. If such combination is possible I guess that a compact device incorporating many junctions inside would be possible (no ?). As for heating: as I said the direct currents are quite small (few µA) and I don't think the generated heat is so great.   

By the way I tried the same method of series connexion with transistors but the problem is I don't know how to operate them. Connecting all the gates together seems not to work (in such case all voltage falls on one transistor).